A children's punning/rhyming game

[Wilson Gray]

On my very first day in the first grade 1942 in Saint Louis, I was
victimized by the following word game:

Q. What's your name?
A. Putting and ta'en!
      Ask me again
     And I'll tell you the same.

This struck me as so hip that I couldn't wait to get home and tell my
mother about. Unfortunately, she, born in Longview, TX, in 1914, was
not impressed, since kids were already running this game on one another
when she was a child.

This little front-off game is so popular and well-known among black
children that it was re-written as a rhythm-&-blues dance song for
adults that was famous for fifteen minutes on black-oriented AM radio
back in the 'Sixties.

So far, I haven't met any white people to whom this is familiar.
Ordinarily, I'd conclude that this game is only a black thing. However,
over the years, I've found it in nursery-rhyme collections directed
toward a white audience. In fact, had I not, I wouldn't know how to
write it out the first line of the answer, since what I've always heard
sounds something like this:

Q. Whutcho name?/whussho name?
A. Putnin tane!
      Ass/ax me agin,
     I teh yuh dih same.

Anyway, are any of y'all white folk out yonder familiar with this?

-Wilson Gray