If I have other characters with exactly same name as current character (either XR or BNet), then current-character-checkmark is also shown for those characters.

This should be easy to fix - just don't show that checkmark for any XR or BNet character.

I don't understand. Do you mean you have multiple characters with the same name and that the checkmark is showing for all of them and is incorrect or just one of them? Or do you mean that I should not displaying multiple characters with same name?

I have multiple characters with same name and checkmark is showing for all of them and not just the one I'm logged in with as it should.

OH I see what you mean. I'll take a look at this. I'll just have to make it only show for the current logged in character based on server. It might be missing the server name check.

Yeah it was a mistake. It wasn't taking realm into account. I have fixed this in the next push.