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.