I think it is just called the name game, or name song.
There are several, but they don't have specific names.
It's Goggle by Tanya Stephans
Names that rhyme with Hannah include Anna, Lana, Rosanna, Diana, Liana, Nana, and of course Montana.
(Don't Fear) the Reaper by Blue Oyster Cult
Every One.
It is a brand name, but Drano rhymes with Plano. Not sure that will fit into a poem or song, but at least it rhymes.
Hirschy (it's a last name)
No animal name rhymes with "trouble".
One girly name that rhymes with Daisy is Maisie.
The name Janette. bet, met, and it if you stretch it a little like in a song
Not many names rhyme with Carter. The name Karter is a form of the name Carter, It means "cart driver" and it rhymes too.
Some names that rhyme with space are Grace, Jace, Ace and Case.
Sac. Back. Lack. Fack, and yes that is a word. Its the name of a eminem song.
Hyatt is the only other name that rhymes with Wyatt. This is a very uncommon name found in the United States.
Southeast kind of rhymes. Is it for a rap song?
Dangerous - Busta Rhymes song - was created on 1997-11-18.
Guys or wise are two names that rhyme with fries.