I don´t usually rename characters and if I do I name them other FF game characters. I have now FF6 playthrough going on where I have renamed characters following way:

Terra- Rydia
Locke- Blank
Edgar-Al-Cid
Sabin- Ward
Shadow- Tseng
Celes- Ashe ( I would have used Beatrix but it didnt fit)
Cyan- Auron
Gau-Guy ( I prefer Gus of Gai but oh well)
Setzer- Luneth ( I regret not using Ingus or Desh)
Mog- Yenke
Strago- Galuf
Relm- Eiko
Umaro- Biran ( havent get him yet but this name I will use)
Gogo- ( havent yet get him)

If I rename summons then I put something really stupid, usually nothing FF related.