Is there a word for someone with the same name?

People (or things) with the same name are homonymous.

The term applies to people who have the same name, as well as books, films, songs with the same title, etc.

For instance the movie version of a book can share the same title of the original book, in which case they are homonymous.

If they have different titles, then they are heteronymous. And the latter also applies to anything or anyone that goes under different names — all of which are true.

If someone goes under a false name, that false name is a pseudonym.

The same way that a different name is a heteronym.

And the same name (the name itself) is a homonym.

Etc.