Unlike the Pokémon trainers, Kaiba has not deluded himself into thinking these are duel monsters variants. Nevermind that he totally used to think they were.. I'm sorry for his names in advance, since the monsters are great!

The winged giraffe are winged-giraffe.
The painters are rejected fur hire. Related to a cardgame archetype. He definitely would not call the creatures this to their faces, because they can be useful.
The dragon-fish are landfish nothing dragon-like about them.. to him.
The pidgey-cat-bunnies are mutated pigeons.
The metal creatures with piranha plants are tin-cans.
The chicken with the human hands for feet he just calls them abominations.

Additions:
The disembodied stuffed animal heads are: Frightfurs
Bipedal chicken/reptiles he's semi adopted Ahsoka's: Blurrgobo but he also thinks of them as Niwatori.
The zummyu/geth is a Mimic.
As for the red flowers that require fire they are Fire-flowers.
Lastly, the spirits inhabiting tools and making a general nuisance of themselves when they are desirous of attention are Jama.