While "protest" is a noun and verb, there's no other word spelled the same with a different meaning.
However, there are some words that are near homographs, meaning they share the same spelling but differ slightly in pronunciation:
* Protest (pronounced PRO-test) - to object strongly to something
* Protest (pronounced PRO-test) - a formal expression of disapproval
Even though the pronunciation is slightly different, it's close enough that some people might consider them homographs.