A bugbear was a sort of a demon who ate small children. Mentions of it exist from the 16th century. It was also used to refer to any object of dread. It bears noting that that the word 'bug' meant something along the lines of 'goblin' or 'scarecrow' in those times.
バグベアー [bugbear] in Japanese.
Final Fantasy III

Level: 9, Number: 023, Type: -, Family: Bear
HP: 110, ATK: 20, DEF: 15, MDEF: 2, STR: 10, VIT: 7, INT: 8, MND: 9, AGI: 9, WGT: 3
GIL: 46 / EXP: 180
Immunity: -
Weakness: -
Resistance: -
Abilities: Attack (uses with 100% chance), attacks once per round
Drops: Potion ~2.4%, Hi-Potion ~0.6%, Phoenix Down ~0.1%
Steal: Potion (99.8% @ THF99)
Place: Canaan grasslands, Tozus surroundings, Nepto Temple surroundings
Drop Rate: 3%
Drop Table: 1 Potion, 2 Potion, 3 Potion, 4 Potion, 5 Hi-Potion, 6 Hi-Potion, 7 Hi-Potion, 8 Phoenix Down
Category: Bestiary