What is it called when words are deliberately spelled incorrectly but pronunciation is kept unchanged?

A general term for intentionally altered spelling is sensational spelling, in which the writer misspells words for an intended effect.

Another, more specific term is cacography, which is misspelling intended for comic effect. It was often seen used to mock illiterate/uneducated people.

It can also be a form of an eye dialect:

The use of nonstandard spelling for speech to draw attention to an ironically standard pronunciation. The term was coined by George P. Krapp to refer to the literary technique of using nonstandard spelling that implies a pronunciation of the given word that is actually standard, such as wimmin for women; the spelling indicates that the character's speech overall is dialectal, foreign, or uneducated. This form of nonstandard spelling differs from others in that a difference in spelling does not indicate a difference in pronunciation of a word. That is, it is dialect to the eye rather than to the ear. It suggests that a character "would use a vulgar pronunciation if there were one" and "is at the level of ignorance where one misspells in this fashion, hence mispronounces as well.

It is called 'phonetic' — it is spelt how it sounds (phonetics is the science of sound). Some of the common phonetic spellings come from the old world English such as GEdgar's contribution. In a lot of cases, I see bastardised versions of this phonetic spelling — which is OK if kept in context, but unprofessional if used indiscriminately.

TV Tropes calls it Xtreme Kool Letterz.

It is called allegro speech.

The deliberate misspelling, respelling, or non-standard alternative spelling of words, usually with the purpose of conveying rapid or informal speech patterns.
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This is also related to the very nature of English language (and most languages) where there is no exact one-to-one correspondence between language and writing. There hasn't been a universal systemic spelling reform in English language also, though there were some attempts. In the end, spellings are made by people and popular choices are eventually adopted by dictionaries . The internet and text messaging are allowing more people to influence spelling than ever before. Also, Britons tend to relate this to Americanism, as nite is originated in U.S. English.

It is explained as below in the book Linguistics for Everyone (by Kristin Denham and Anne Lobeck):

Often words are misspelled--or respelled, as it's sometimes called when it is done intentionally--not only in informal email messages but in more public, 'edited' spaces. These respellings, such as in the following examples, also known as allegro speech, indicate informality.

gonna, dunno, wanna
nite, lite, thru

The spellings of these words are all in a state of transition with respect to their acceptability as standard spellings. At this time, most people view them as nonstandard but intentional spellings; thus they differ from simple misspellings. However, this usage is restricted mostly to informal writing or print situations. . . . The variations usually coexist for some time before one becomes dominant and the other drops out. For example, the use of nite remains fairly restricted right now; its use may increase over time, and eventually the spelling night could drop out of the language.

From a phonetics standpoint, the spelling change from night to nite is related to the silent digraph gh. The below excerpt explains the relationship between sound and graphic sign from a linguistic standpoint and includes our example. (from the book Historical and Comparative Linguistics By Raimo Anttila)

This imperfect match between sound and graphic sign makes the changes in either one independent of each other, just as in the linguistic sign, the lack of one-to-one correspondence between sound and meaning makes sound change independent of semantic change. Thus a change in spelling (e.g., through > thru, or night > nite) does not necessarily reflect a change in pronunciation directly. (But, of course, such spelling changes are often made possible by pronunciation changes somewhere in the history of language. Thus write and right faithfully record an Old English contrast between [wr] and [r], while right currently has a spirant [x] in some English dialects even though it was lost in Standard English in the fifteenth century.)

Texting abbreviations are obviously the most commonly mis-spelt versions of many words but understood and pronounced correctly. eg: sis m8 go2 ny 2moro

I don't think there is a single word answer. As you can see from this Venn Diagram, the point where the blue and red circles overlap (same meaning/same pronunciation/different spelling) there is no single word credited.

This is likely due to the fact that it happens very rarely.

In her paper "Spelling-Manipulation and Present-Day Advertising," Louise Pound calls this phenomenon by several names:

• spelling-manipulation
• re-spellings
• spelling-perversions

Pound theorizes that originally, a few advertisers used this to catch consumers' attention, as the incongruity of seeing "Nite Lite" or "EZ Walker" instead of the expected spelling would make them do a double-take and latch the product name to their memory. Eventually, many more advertisers jumped on the bandwagon, and now the practice is so common (This article lists a bunch of them) that people rarely think anything of it anymore.

Metagraphy [1]2

The rendering of letters of an alphabet of one language into the possible equivalents of another; transliteration.

Just unconfirmed (according to Wiktionary).

I knew what orthography was (the conventional spelling system of a language) and understood that ortho is the Greek etymological root for 'straight' (orthography meaning 'straight writing'). There is no direct opposite for ortho, but there are two slant opposites. Para and meta. Coupled with graphy (the Greek root for words/writing), I decided to look up these words.

paragraphy sounded strange. I looked it up and found that it meant something else entirely, so that left metagraphy.

Typoglycemia

found on Wikipedia