Wow, there are so many for Alex! And the cool thing is, is that he responds to almost every one

Ok, here are the ones I can think of:
Aly, Aly Bear, Bear, Mister/Meester, Mister Bear, Boy, GoofDog, Schweetie, You, Buddy, Boudie, Bew, Puppy, Bud, Ew Ew Birdie Sha BooBoo(), Beer(a form of Bear)

That's all I can think of right now, if there's more, I'll come back