Should it be humanoid or an animal with one eye that has traits of a cyclops?

Make water/fighting, because Cyclops are related to Poseidon and maybe give it an ability that ups its attack whenever it's hit with fire attacks because Cyclops worked in blacksmiths so fire would probably give it strength

Ability: Ember Typhoon
Raises the Attack stat if hit by a fire-type move.

Yes

Make it water, fighting type
Make it look more humanoid but like- monstrous

give it 1 eye

It should also be a dark type.
It will herd Wooloo / Market

That would be cool
Or it could be water type since in Greek mythology the cyclopses are related to Poseidon

Fighting / Dark

What should it's name be?

IDK.

Depends on how it looks. For a more accurate representation of Greek mythology and sticking with Fighting/Dark, maybe something like Nerogue (二ローグ)

Make it either Fighting/Dragon or Fighting/Dark

Your mom

fighting/water,sv event ONLY,tera type is fire,fla sh fire is ability,some sort of special that can burn