Are nicknames a good thing to have or should we all be called by our full names?
I think that real names are very important since they hold a lot of meaning especially if it comes from the Torah or named after someone great.
Chanoch is also called Mem Tet. Shem is also called Malcheitzedek. Shlomo Hamelech is also called Yedidya.
Oh yeah and for the feminists out there Devorah is called Eshet Lapidot.
So Nicknames are probably seen as positive even in Judaism. They simply need to have a real Mashmaut Ivri to be embraced as such and not a form of moshav leitzim which kids and immature adults do to harass each other.
My understanding is that if someone is named after 2 people and using a nickname or shortened name causes one of those names not to be used and therefore one of those people named after to be forgotten, then it is not a good thing. Otherwise it is fine. Personally I generally call all of my children by their full names.