For Snarf, at least, in-universe his real name is Osbert, but he found this embarrassing and went with his species name instead.
Quote from the episode "Feliner Part 1"
Snarf: Who are you? How did you get here? You're a Snarf. How can that be?
Snarfer: [panting] One, one question... at a time, Uncle Osbert.
[runs over and whispers]
Snarf: Sh! Don't say that. I hate that name. No one calls me Osbert. "Uncle Osbert"?
Snarfer: I'm Snarfer.
Snarf: Snarfer? My nephew Snarfer? That's impossible.
Snarfer: It's true.
Snarf: But you're just a baby... Oh... I must be getting old. That was years ago. Snarfer!
[they cheer and dance around for a moment]
Snarf: But never call me Osbert, OK? I'm Snarf. Just Snarf.