It depends. I have named all my cats, my dogs, etc in life. But my exboyfriend has a cat named KatKat. Was he loved any less because he had a fake name? nope. He still got love, food, vet care just as any other properly named pet. Sometimes you just don't have any creativity in naming them, so you call it puss or pup hoping someday a name will strike you... and in the meanwhile Puss or Pup is what his name becomes.

My betta has no name. I typically refer to him as Fishie. Like when I tell the cats to "stop drinking Fishie's water!" Does it mean I care less for my betta because he's nameless? nah. I just couldn't come up with a name I liked... especially since I swore he wasn't going to last the weekend with the cats. Here he is months later still happily swimming in the water that gets refilled every day because the cats prefer to drink from his bowl (extra flavoring perhaps?) and now the betta's unoffical/official name is Fishie.