My lovable Persian-mix "Puff" is also:
Puff Puff
Puff-a-lump
Puff-a-luffagus
Puffa Roach (from the band Papa Roach)
Puff the Luff Luff (no idea how that started)
Puff the Magic Kitty
Pufferino
La Puffiere

I sing to her too, but not real songs. Somehow I made up this song "You're the puffiest fluffiest puff of all the puffs in all the world" and I seem to be the only one who can sing it right. She comes running! Another popular phrase is "Are there any Puff-puffs home?" to which she'll meow from the other room. This forum is hilarious, and I'm so glad I got to share!