Is it CoViD? Or COVID? Covid? How should the word be spelled?

COVID-19 stands for "Corona Virus Disease 2019" (ref.); therefore it is an acronym and should be treated as such.

"Covid-19" seems to have acquired much the status of a regular word already; "covid-19 is pronounced /kəʊv ɪd naɪn 'ti:n/ in RP and /'koʊvɪd nain 'tin/ in American English (ref. 1'35); so it should be written in lowercase letters and capitalized where nouns are usually capitalized. As well one should be allowed to write it in uppercase letters. Those three forms corresponding to that of a common noun are mostly the forms found on the web: "covid-19", "Covid-19", "COVID-19". The following particular treatment of this word as an acronym is likely to be applied.

Some publications choose to capitalize only the first letter of acronyms, reserving all-caps styling for initialisms, writing the pronounced acronyms "Nato" and "Aids" in mixed case, but the initialisms "USA" and "FBI" in all caps. For example, this is the style used in The Guardian,[69] and BBC News typically edits to this style (though its official style guide, dating from 2003, still recommends all-caps[70]). The logic of this style is that the pronunciation is reflected graphically by the capitalization scheme.

Some style manuals also base the letters' case on their number. The New York Times, for example, keeps "NATO" in all capitals (while several guides in the British press may render it "Nato"), but uses lower case in "UNICEF" (from "United Nations International Children's Emergency Fund") because it is more than four letters, and to style it in caps might look ungainly (flirting with the appearance of "shouting capitals").

Small-caps variant
Small caps are sometimes used to make the run of capital letters seem less jarring to the reader. For example, the style of some American publications, including the Atlantic Monthly and USA Today, is to use small caps for acronyms longer than three letters[citation needed]; thus "U.S." and "FDR" in normal caps, but "nato" in small caps. The acronyms "AD" and "BC" are often smallcapped as well, as in: "From 4004 bc to ad 525".

Official nomenclature and journalistic practice

A recent item by Elisabeth Ribbans, "COVID or Covid? The comfort of pedantry at a time of national crisis," in The Guardian (April 19, 2020), asserts that initial-capping acronyms (abbreviations pronounced phonetically as approximately the sum of their letter sounds, rather than as as a series of names of the constituent alphabet letters) is the prevailing style at "most British newspapers":

I fell into happy correspondence the weekend before last with a medical specialist who wanted to know why the media was “incorrectly” spelling COVID-19 as Covid-19. I explained that, like most British newspapers, the Guardian’s style is to use uppercase for abbreviations that are written and spoken as a collection of letters, such as BBC, IMF and NHS, whereas acronyms pronounced as words go upper and lower, eg Nasa, Unicef and, now, Covid-19. The reader was remarkably understanding given that her query turned out to be more than passing curiosity: she was busily correcting scientific articles by authors who’d adopted the media’s style. We each apologised for having caused the other work and moved on better informed about our respective fields.

The International Committee on Taxonomy of Viruses has an interesting undated news item titled, "Naming the 2019 Coronavirus," about the naming of the coronavirus responsible for COVID-19, which it calls "severe acute respiratory syndrome coronavirus 2," shortened to "SARS-CoV-2." Note that "SARS," like "COVID" is generally pronounced as an acronym, not as an initialism, and yet the ICTV renders it in all caps but renders the "CoV" part of the virus name (which is short for "coronavirus") as mixed uppercase and lowercase. The ICTV item then continues as follows:

The disease name (which in many cases is different from the virus name) has been designated as COVID-19 by the WHO. The '19' in COVID-19 stands for the year, 2019, that the virus was first seen. The number '19' has nothing whatsoever to do with virus strains, genotypes, or anything else related to the virus' genetics. The virus name was announced by the World Health Organization on February 11, 2020. See the February 11 World Health Organization Situation Report. This clearly states that "WHO has named the disease COVID-19, short for 'coronavirus disease 2019'.”

So the World Health Organization and the ICTV appear to be aligned on the formatting of the disease name as all-caps. This explains why the medical specialist was at odds with The Guardian writer/editor over the treatment of the acronym COVID-19.

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Newspaper guidelines for formatting of 'COVID-19'/'Covid-19'

It's tempting to view preference for spelling acronyms as all-lowercase or initial-capped-only words as peculiar to British journalism. Certainly, the New York Times (for example) doesn't follow The Guardian in spelling NASA as Nasa—but its style for dealing with acronyms is far from consistent, as these consecutive entries in The New York Times Manual of Style and Usage, revised edition (1999) make clear:

NASA for the National Aeronautics and Space Administration.

Nascar for the National Association for Stock Car Auto Racing.

In fact, NYT also endorses (on the one hand) Nasdaq, Unesco, Unicef, and Waves, and (on the other) NATO, OPEC, OSHA, PATH, RICO, and WAC. It shows similar inconsistency in formatting some initialisms (such as N.A.A.C.P., N.C.A.A., N.L.R.B., N.Y.U., and P.S.A.T.) with periods, and others (such as NOAA, NPR, PTA, SAT, and SUNY) without.

As it turns out, there is actually a slender thread of logic behind the split in the NYT treatment of, for example, NATO and Unesco:

acronyms. An acronym is a word formed from the first letter (or letters) of each word in a series: NATO from North Atlantic Treaty Organization; radar from radio detection and ranging. (Unless pronounced as a word, an abbreviation is not an acronym.) When an acronym serves as a proper name and exceeds four letters, capitalize only the first letter: Unesco, Unicef.

COVID is more than four letters long, so NYT style for acronyms would dictate spelling the disease name as as Covid-19—just as The Guardian does, albeit for a different reason—and that is in fact what it does.

The style guideline for acronyms in The Associated Press Stylebook (2007) is very similar to the one in New York Times, with one critical difference in detail:

Use only an initial cap and then lowercase for acronyms of more than six letters, unless listed otherwise in this stylebook or Webster's New World College Dictionary.

Because COVID is five letters long, it triggers the Covid spelling according to NYT style but the COVID spelling in AP style. My local newspaper, which follows AP style, thus uses the form COVID-19.

The ever-whimsical stylists at The New Yorker, take a third way, setting COVID-19 in small caps (_^COVID-19)—a practice that the magazine follows with all acronyms (as opposed to initialisms), regardless of their length.

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Book style manual guidance for formatting acronyms

Moving now to book style guidelines for acronyms, I find far less inclination to adopt a length-based difference in formatting. The Oxford Guide to Style (2002), for example, has this comment about differential treatment of acronyms by length:

Any all-capital proper-name acronym is, in some house styles, fashioned with a single initial capital if it exceeds four letters (Basic, Unesco, Unicef). Editors should avoid this rule, useful though it is, where the result runs against the common practice of a discipline (CARPE, SSHRCC, WYSIWYG), or where similar terms would be treated dissimilarly based on length alone.

The Chicago Manual of Style, sixteenth edition (2010) seems even less inclined than Oxford to endorse length-based all-caps versus initial-cap-only decisions:

10.6 Capitals versus lowercase for acronyms and initialisms. Initialisms tend to appear in all capital letters, even when they are not derived from proper names (HIV, VP, LCD). With frequent use, however, acronyms—especially those of five or more letters—will sometimes become lowercase (scuba); those that are derived from proper nouns retain an initial capital. Chicago generally prefers the all-capital form, unless the term is listed otherwise in Webster's.

[Example:] NAFTA (not Nafta)

This view puts Chicago squarely in the COVID-19 camp, whereas Oxford's position is harder to anticipate and may be determined by situational considerations—for example, if a book mentions AIDS, Oxford might be more inclined to render the novel coronavirus disease as COVID-19 for consistency, despite the purported usefulness of the five-letters-or-more rule.A quick check of Merriam-Webster's Eleventh Collegiate Dictionary (2003) reveals that NASCAR, UNESCO, and UNICEF all receive all-caps formatting in their entries; the Eleventh Collegiate and MW Online don't have a separate entry for Nasdaq, but most references to the acronym in the online dictionary initial-cap the term.

Webster's Standard American Style Manual (1985) confirms that MW has no interest in length-based rules for handling acronyms:

Most abbreviations that are pronounced as words, rather than as a series of letters, are capitalized. If they have been assimilated into the language as words in their own right, however, they are most often lowercased.

[All-cap examples:] OPEC; NATO; MIRV; NOW account

[All-lowercase examples:] quasar; laser; sonar; scuba

Webster's includes no examples of acronyms that it would render in initial-cap-but-otherwise-lowercase format. So even if MW weren't inclined to accept the WHO's preferred all-cap formatting of COVID-19 (which I think it would be), there is no reason to suppose that it would endorse the form Covid-19.

In the course of a fairly lengthy discussion of acronym and initialisms, Bryan Garner, Garner's Modern American Usage (2003) has this to say about capitalization:

[C]apitalization raises various questions. In AmE there is a tendency to print initialisms in all capitals (e.g., FMLA, NJDEP) and acronyms in small capitals )e.g., _^GAAP, _^MADD, _^NASA). Some publications , however, use all capitals for both kinds. But in BrE the tendency is to uppercase only the first letter, as with Ifor and Isa for Implementation Force and individual savings account. An influential British commentator once suggested (with little success on his side of the Atlantic) that the lowercasing be avoided: "From the full name to the simplified label three stages can be detected. For instance, the Society {for Checking the Abuse of Public Advertising} ... becomes first S.C.A.P.A., then SCAPA, and finally Scapa. In the interests of clarity this last stage might well be discouraged, since thereby the reference is made unnecessarily cryptic." Simeon Potter, Our Language 177 (rev. ed. 1966). American writers have generally agreed with this view.

Like Merriam-Webster, Garner doesn't acknowledge the length-based differential treatment of acronyms cited in such guidebooks as AP, the New York Times, Oxford, and Chicago.

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Conclusions

The reason you are likely to see different formatting choices for COVID-19 is that different publishers base their formatting choice on different rules. Publishers that opt for COVID-19 may simply be using the form preferred by the World Health Organization in, for example, Situation Report — 22 (February 11, 2020):

Following WHO best practices for naming of new human infectious diseases, which were developed in consultation and collaboration with the World Organisation for Animal Health (OIE) and the Food and Agriculture Organization of the United Nations (FAO), WHO has named the disease COVID-19, short for “coronavirus disease 2019.”

Others that favor COVID-19 may be following the standard US book publishing style of using all caps for acronyms of any length, or Associated Press Stylebook style, which calls for all-capping acronyms of six letters or less.

Those that favor Covid-19 may be following the Guardian style preference for initial-capping any acronym, the New York Times preference for initial-capping acronyms of five letters or longer, or general advice to the same effect from (for example) Oxford University Press.

And those that favor _^COVID-19 may be enforcing an older U.S. book style preference or be responsible for editorial choices at The New Yorker.

The option of using CoViD-19 may appeal to publishers that want to indicate where the word breaks in the original phrase fall—but in choosing this mix of capitals and lowercase letters, they don't appear to be on the strongest ground, technically speaking, since coronavirus is generally spelled as a single word. (Although Merriam-Webster dates the term to 1968, coronavirus didn't debut in an edition of the Collegiate Dictionary until the Eleventh Edition (2003)—and it did so then as a single word.) It follows that only the C (for coronavirus) and the D (for disease) are markers of separate words. A publisher attempting to be true to the source words of the acronym might therefore do better to adopt the form Co'vi'D-19 (a form that, as far as I know, no one uses, perhaps because it looks ridiculous).

I agree with The Economist (covid). It has to do with the frequency of use. Similar to radar and laser, covid has become an everyday word. It is also a combination of not only first letters but a mixture of 'first and second letter' and 'first letter' only. It does not have to follow the rules for SARS (which is an inititalism: first letters only).

Covid-19 is an acronym based on the name Coronavirus disease (2019). It is not an initialisation since a) it is pronounced as a word and b) it is not composed of initial letters of words. Coronavirus is one word. The "Co" of Covid come from the "Corona" part, the "vi" from the "virus" part and the "d" from "disease".

For the acronym to be written in all-capitals, each letter should be an initial letter, as in NASA. In this case, only the C and D are initial letters. Since it would look stupid to write "CoviD" or "CoViD" if you wanted to treat "coronavirus" as two words, "Covid" is the logical choice.

Please note that, unlike "radar", "Covid" is a proper noun and should therefore start with a capital letter.