hydra was a fearsome beast with multiple heads, one of which is immortal. Naming a group after it was just to indicate the power of the party, and it's invincible leader:D
Hydra where the team sent to find out what the hell was going on and got sucked in to this "other world" after they got there they one by one got turned in to shadows of there former self's
In case ya haven't noticed, there's an entire set called Hydra, it's found throughout numerous other games, and there's a Hydra <jobname> of every class, minus the 3 new ones.