Hmm, but going off of your thought, could it be that we (the players) have the ability to choose Tidus' name because we are actually the fayth? We create that identity for him and watch as the dream plays out.
YES. That is a great theory. I mean, it's pretty much true, innit? As soon as we stop playing, he ceases to exist. Hell, all of Spira does, so maybe we're an offshoot of Yu Yevon?!?!?