I really miss being able to change ALL of 'em, like you could in FF6. Give us that, or give us complete unchangeability (like in Xenogears etc), because it's pretty disappointing when you get to do one ... then everyone else is fixed.
Mind you, it can get confusing. By the time we reached a point in that game, me & my bro had forgotten what each character's original name was, and it took a bit more digging to match names to pixelated faces (this was wayyyyy back when zSNES was quite new and the internet wasn't so comprehensive or easy to search). I think this may be what led to him keeping all the default names in his game of FF7...
As for how we chose them ... just whatever seemed appropriate for the character's appearance and manner. EG Locke became the (far less pronunciation-ambiguous) "Indy". This is sort of how I still do it, though occasionally some kind of stupid theme-naming will creep in, or I'll pick whatever the most obvious feature of a new but poorly defined character is and twist it for laughs. The aeons in FFX have a bit of a combination of the two (Flux, Mr Bitey, etc)... and the lead character?
Well, he was pissing me off for quite a while before the naming opportunity arose, and not realising he was going to be the only one ... I called him Bumcakes. I think I might have nicked it from Yahtzee... dunno. The idea certainly passed through ZP-ville on its way thru my brain. It remained fitting for an infuriatingly long time, and only quite a way into the game did he start getting mature enough that I sort of regretted it. Sorta. I'm just going to explain it away as being an Al Bhed cypher-name from now on.
(...
SO woulda called Wakka "Pac Man". Yuna "Aerith", Rikku "Yuffie", Auron "Vash", etc. You knows it.)
edit: Next time I think I'll go with highly gender/culture-inappropriate names. Maybe reprise a few from really old RPGs (Onionkid, Jamseed/Ahriman/Zahhark/Genie/Prince (& Princess?)/Saleem/Agmar

). That or just call each one "you" ("he", "she", "it").