I usually keep the default name. I just can't take the game seriously otherwise. Though when replaying certain Final Fantasy games where one character goes by a nickname (Red XIII or Dagger), it can be fun to use their real name instead. Or just name them something silly - they are practically asking for it anyway.
I did name Red XIII "Spot" once. Also, when my friend was playing FFIX and asked me to come up with a better name for princess Dagger, I suggested "Wedgie". Anyone who's seen her standard outfit from the back will understand why. These days, he always has trouble remembering the names of any FFIX characters, but any time the princess is mentioned, he identifies her as Wedgie right away!