Well, if you want a blatant parody of FNaF, the animal species in that game were a fox (Foxy), a chicken (Chica), a rabbit (Bonnie), and a bear (Freddy). (Not counting Balloon Boy, unless you count humans as "animals".) But if you want to avoid being too close to the FNaF games, you could go with a wolf, a cat, a lion, a monkey, a gorilla, or a human, just to name a few. (All of those have been done before by various pizza restaurants.)
If you go with a lion, then Lionman would be a good name, as well as being a Mumford and Sons reference. Or if you choose a human, then maybe Humanman (just because of the sheer stupidity of the name)?
As for an attack, throwing its head (Golden Freddy in FNaF 2), biting the enemy's head (Golden Freddy in FNaF 4), or slapping the player really hard (Chuck E. Cheese in this video) are all options. Or maybe something involving electric shock and a joke about faulty wiring?