I think thats works best for the nerrative, but GFs are explicitly referred to as pets in this game.

Quaicotle : Puppy (cute like a puppy)
Shiva : Stacy (reminds me of a cool girl I knew)
Ifrit : Burke (after Chainers first summon in MTG novel)
Siren: Lichelle (reminds me of adult film star Lichelle Marie)
Brothers : J and K (Men in Black)
Diablos : Randall (yes, Randall Flagg)
Carbuncle : Cootie (my girlfriends cat)
Leviathan : Sephiroth (lack of anything better...)
Pandemona : Deckard (protagonist of Blade Runner)
Cerberus : Tribble (Tribble, Triple, I like Star Trek)
Alexander : Rambrandt (classical figures)
Doomtrain : Akira (that kid in the cyberpunk classic)
Bahamut : Jace (MTG reference)
Cactaur : Tex (mustache...)
Tonberry : Darwin (no good reason)
Eden: Elvis (king of GFs, King of rock and roll)