Does the name have an origin prior to Podkayne of Mars? A meaning?
Podkayne at Google ngrams, 1650-1965:
The peak at 1957 looks to be a glitch based on a publisher rejiggering one of the Heinlein anthologies. 1963/64 is the original serialization and publication of the story. The absence of any other literary ref in the previous 300 years makes it look pretty likely that Heinlein came up with the name himself.
There's an earlier version of Poddy in Heinlein's "Puddin'" stories. The only one I've read is "Cliff and the Calories" which is good, but not sci-fi.