I have/had homage characters. I find the fun is getting across who they are meant to be without making them look nearly identical nor having the same name. For instance, a few people will know why my Captain Marvel homage was called Cap'n Miracle. Others won't. To me that's an interesting way to find people who have experienced/enjoyed the same stuff I have.
If you're just gonna name 'em the same and make them look the same, that, to me (and this is just me me, not anything official) seems kinda low effort / lazy. but some people wanna be the 900th incarnation of Wolverine or Superman so... okay I guess. If that's fun for you, go for it.
But it _is_ worth noting that the original devs did work things so that most of your costuming options can't be identical to a known copyright character. Sure, some things are VERY VERY similar.... but not identical. You might say you are Captain America or Superman or whatever, but most folks will know by looking that you aren't.