Haha. Yes, the other characters know his name; he's called "Tidus" (or whatever you choose to call him) by several NPCs, in text-only conversation. One or more of the Besaid Aurochs use his real name, quite early on.

Personally, I think it's pointless having the ability to change a character's name if that name is never gonna get used outside of the status screen.

But if they hadn't included the option of changing his name... oh, I can just imagine the "hardcore FF gam3rz":

"OMG DIS IS NOT A RAEL FF! CUZ U CANOT HCANGE DA CHARS' NAEM!!! IT R SACRFILGEE(?SP??????)!

I H8 U SQUARE, U RUIN AL MY GOOD GAEMS!!!!!

IN AL DA RAEL FF U CAN CHANEG TEH NAEMS1111!!!!"

...and so forth.