Is there a word that means "as its name would suggest"?

I think the short answer is No.

The long answer (as its name would suggest) is that there are lots of words and phrases which in context mean as [that name] would suggest. Such as obviously, self-evidently, as you can guess, unsurprisingly, etc. But as you might expect, none of them are really necessary, since you're already assuming the hearer knows what you're saying anyway.

Notwithstanding Shakespeare's observations on What's in a name, people usually do try to assign meaningful names to new things that need naming. We can't really do that with babies, because we don't really know what they will be like when they grow up. But marketing departments, for example, spend a lot of time trying to come up with names that somehow suit their new products.

Although not strictly English, the Latin phrase "nomen est omen" (literally "the name is an omen") seems to get the message across. I would much rather stay away from Latin, hence how I found this page.

Eponymous, the adjective form of eponym: one for whom or which something is believed to be named. Merriam Webster Collegiate Dictionary.

Computer Science is the eponymous science of computation.

In the case of a person's name there is "aptronym", meaning a personal name aptly or peculiarly suited to its owner, such as a rich person with the last name of Flush, or a hairdresser whose last name is Cutter.

Reference: Wikipedia, Aptronym:

Aptronym, aptonym or euonym are rarely-encountered neologisms for the concept of nominative determinism, used for a personal name aptly or peculiarly suited to its owner; essentially, when someone's name describes what they are or what they do.

In the book What's in a Name? (1996), author Paul Dickson cites a long list of aptronyms originally compiled by Professor Lewis P. Lipsitt, of Brown University. Psychologist Carl Jung wrote in his book Synchronicity that there was a "sometimes quite grotesque coincidence between a man's name and his peculiarities".

I've been in several situations which made me which I had a shorthand for "as the name suggests". After much digging around and finding nothing, I figured that the English language need not constrain itself to commonly used combinations of roots and _fixes. I've coined "nomenous" for this.

"nomen" -- the Latin root for "name" or "title", and "ous" -- the Anglo-French from Latin "osus", meaning "full of" or "having the quality of"

So...

Nom•e•nous

adjective

having qualities suggested by its name

"My TI-503 is a nomenous calculator"

Now we need an adverb form of it... "nomenously"?

How about xxx personifies its name by...(doing as it's name suggests)...