What should I do if someone is using my name ?

I believe those characters are allowed on EU server, but not US. If it's that big of a deal to you, play on US servers. Problem solved.

its not...but text can be sent on the chat that makes it appear to just glancing eyes that someone with your name is saying...anything...abusive or racist, sexist... silly..insulting...if you were to watch the text scroll word for word you would notice it was 2 people...but who reads chat word for word ...most just glance while playing...

Lol, so you reported someone for having the name Batman? Maybe stop and think before you make a frivolous report next time. You can steal anyone's name on this game, at all.

Example, my main Black Prime, my villain alt BIack Prime. I made the L in black a capital I, but it's not the same name.

This requires a change by DBG... and is a bit of a pet peeve... the font used for character names is unclear. Lowercase L and uppercase I look too similar... and in the OP's case, the font cannot display the characters used by the second player. So if you have a problem with a player you could end up reporting the wrong person because you confused an I and an L... or something like that... since you cannot do a "Recent Text -> <choose name> -> Report"

If my name was Bob Finger or Bill Kane, I might be, but you're not the originator of the character. You're like the one kid out of fifty on the playground that wants to be Batman.

So. Does. Everybody. Else.

I was extremely confused by what this was about until towards the end of the first page, and once I saw what it was about...seriously? Have you never played an MMO before? Older players, like me, had to suffer a _NF being attached to names we’ve had since *launch* and you are complaining about some nonsense where someone’s name looks like yours because they altered some characters? And the fact that you visually have exactly the name you want for your character is maddening to me, because in the US, we don’t have that option *and* we got a big middle finger with the whole server merge suffixes.

And you’re honestly worried about looking bad in chat? Does anyone even pay attention to chat? Does anyone even use general chat except spammers? Chill out. Nobody is going to make you look bad because nobody cares about you in this game. Nobody cares about me either, in case you think I’m trying to insult you.

TL;DR: Wow.

Not sure how it is your name if someone else is already using it.

But it's not your name, you and waaaaaay too many other little wannabies are using the name of an already established character (in this case Batman) so you have absolutely no/nil/zero/nada grounds for complaint when another player decides he/she wants to cosplay as Batman (or whomever) as well.