A Beastmaster would not transform into a monster. That would be the Morpher job from Final Fantasy Tactics. Beastmasters control monsters, Morphers turn into them.

That said, almost every job/class released in this MMO has also made an appearance in a Tactics series. I think the only except is Arcanist or Astrologian (which I am in the camp of describing it as a renamed Time Mage). So, Morpher does not seem out of the ordinary to me with the Spiderman hint. He is a man that is also a spider.

However, Blue Mage makes more sense to me, so...