Popular vote is going for Aeris, and that's what I'm likely going to be using. But we'll keep this up I suppose a little while longer.
"Red XIII" is rarely spoken in the game, and in the few cases it is, jack.o.lantern and myself will likely come up with a substitute such as "Red" instead of "Red Thirteen", which sounds like a robot. His default name will remain the same, so in his captions you will see "Red XIII", but again when his name is actually spoken, we'll see about using something less clumsy.
There's a problem with this, however, and something everyone needs to consider. When Red XIII's name is spoken, it uses the {RED XIII} tag. In order to change what is spoken, it would have to be hard coded so that no matter what you name him, it will still come up simply "Red" or whatever. I'm personally not going to use Nanaki. The revelation of his real name is an original piece in the game, and to simply default him as "Nanaki" takes that away. It's safe to say we're open to suggestions on this, but Nanaki won't cut it.
On the other hand, at the time you acquire Red XIII as a party member, keep in mind to a new player he's still just this weird experiment creature, so Red XIII doesn't seem quite so stupid. It seems dumb if you already know him as Nanaki, son of Seto etc. But originally he starts out seemingly a strange experiment. Just something to keep in mind before dismissing "Red Thirteen."