What I would assume (without seeing any code or any known issues) is that when they are changing their rpname, the old name doesn't get overwritten, just changed. If that's the case (I'd guess, I'm not the best at DarkRP stuff) then you need to find someway that makes it when their rpname changes, to completely overwrite their previous name. I believe the issue would that; they're changing their name but their previous name is still in a table of sorts. You need to make that old name be removed when they change it.
I could be wrong, I'm not great with DarkRP.