I use the character's names. The only time I don't is when it's a third version, like Emerald or Platinum. I only remember the name I gave my guy in Platinum, which was Yuuto. If there's a Z I'll probably finally go with Reindeer.
I did a trade between my X and OR and it was just so weird. 'Marina would like to trade with Marina' 'Would you like to add Marina as a friend,' as you can see I haven't met any other Marina's in my lifetime...
This question made me want to check my games to see what I did as a kid versus now, but I didn't seem to stray from several names. This from versions I completed myself... The other games like Gold, Leaf Green, White ,Y, etc were completed by either my brother or my husband so I didn't count those lolz
I use my real name unless I want to play through a specific game with the name of a character from the anime to use their pokemon in the playthrough. Such as in Platinum. I was Dawn with her pokemon. Piplup, Buneary, Pachirisu, Mamoswine, Togekiss, and I traded myself a cyndaquil egg so it would have her OT
My trainer name is Chris. Yea, not very original using my own name...
My excuse with X&Y though is that I heard you can have two names (the other being your nickname) which I set as Tao. Sadly, I wasn't aware of just how little the 'nickname' gets used.