You know the preferences file? You can find it in \Rome - Total War\EB\preferences. There's an option there that says something like "show character names" or something like that (can't check the actual wording since I'm not on my gaming computer right now). I'd bet that one says "TRUE". Change it to "FALSE" and that should do it.
Edit: It's possible it says "LABEL_CHARACTERS" or something like that.
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