It also used in Warriors Orochi 4, after Ares says that they must hurry because of Yggdrasil is almost complete. If you play another character until they saw a strange tree, it reminds them of defeating Hydra from previous game.
Hydra Is The English Name For Simplification. Localization Was Heavily Pressured To Conform To Western Audiences. Keeping The Name As Yamata No Orochi Would Confuse English Players. At Least That Was Their Logic.