Although I'm crashing quite a bit, I did manage to see some pet-related changes. The spellbook companion tab is now gone completely, leaving only the Pet Journal. Also, the "Info" icon in the journal now tells you the source for the companion.
It's strange though, because although I know many of the pets, all of my companions in the Pet Journal are greyed out. I can't seem to summon them through the Pet Journal atm. I'm wondering if I need to train for pet battles from a Pet Trainer before I can even summon any of the pets I already have. That's a bit ridiculous, though.
It could just be due to developers needing to turn off certain aspects of the Pet Journal to implement and address systems and features for pet battles. We'll see once the beta servers stabilize and I can stay logged in for more than a few minutes without crashing. (I did read somewhere that a Pet Trainer was found in Goldshire, though. I'll have to try and check that out once the crashing stops.)
In other news, the Can I Keep Him? and other collect X number of pet achievements is showing up in the new Pet Achievements tab, so no worries. Players should still be able to earn those pet rewards for the number of companions they collect. Whether or not the same numbers that currently apply to these achievements (50, 75, 100, etc.) will also apply in MoP, I don't know. As a few others have mentioned, collecting 50 pets seems hardly an achievement with the prospect of over 400 possible pets to collect in MoP.
That's it for now until the crashing stops.
UPDATE: A Pet Battle Trainer is in Goldshire! His name is Marcus Jensen. It currently costs 80 gold to train and requires level 5. Track pets currently costs 8 copper and requires level 5. Prices and minimum requirements are subject to change lol.
Oddly, I still can't summon my companions or add them to my battle team even after training. All companions in the Pet Journal are still greyed out. It might be bugged.
Oh, and there's a new cursor when hovering over wild pets. It looks like a paw print heh.