Hmm, well, the titles are interesting because they imply something about the world or story, even if the game unfortunately doesn't actually deliver on that implication. Your concept suggests lots of good words: alpha, ascension, lupine, wolf, leader, challenge, struggle, pack, destiny, orphan, alone, abandoned, pup, hierarchy, earn, reclaim...
You could call it Lupus Rex, Packsong, ProvingGrounds, Wolf's Proving, Wilderness Proof, Wilderworthy, Wolf's Worth, Survive&Reclaim, Alpha's Claim, Claim&Climb, Animal Ascension, Earned Ascension, Alphascension, Pup's Place, Archy Outcast, Packceptance, Bandon, Bandoned, Saken (was trying to convey the concept of a character who un-abandoned themself in a proactive way instead of being rescued or adopted by someone else, but not sure how to say that...)
Just out of curiosity, have you seen the anime series Useless Animals (Damekko Dobutsu)? I liked that series, it was a lot of fun.
Now these are some suggestions I seriously considered. Some of them sounded a little ridiculous though. Haha. Ones I liked specifically were Alpha's Claim, Animal Ascension, Archy Outcast, and Alphascension. I got some feedback from friends and it's more geared towards Alpha's Claim. I'm a little conflicted with these names though. It does hint towards the singleplayer a lot, but it may give the impression that the multiplayer is only about wolves' as well when in reality it has multiple species. The multiplayer is probably a stronger point for the game than the singleplayer. So the question is should the title be aimed towards still the singleplayer or represent the game as a whole? Also, I haven't seen that anime. I'll have to check it out sometime.