The Vita isn't called PSP2 for the same reason the Xbox 360 wasn't called an Xbox 2: there was already a system out with a number 3 in the name. So to avoid launching a PS2 months after Nintendo launched a 3DS, they're naming it Vita, so the general public won't subconsciously compare the two consoles that way (3>2).
That was mostly tongue in cheek.
More seriously, Sony's starting to give their products names instead of just product codes. Just look at their phones lately. Xperia, Cedar, Aspen, Vivaz, Yendo, Aino? "Vita" kinda fits right into the naming scheme.