My mother named all her aeons random fantasy names like "Varrell" and "Baruka," but dad named them as follows (in all caps):
Valefor: BIG BIRD
Ifrit: HOT PANTS
Ixion: SPARKY
Shiva: MADONNA
... and I left Utah before he got to Bevelle, so I don't know what he's named Bahamut.
Mom did, however, named Tidus Ali Öops.