There are many variations, but I presume there was an initial original version of puppet stayman.
Does anyone know who came up with it, and why it is named as such?
(A google search has been unrevealing)
According to Wikipedia:
Puppet Stayman, initially developed by Neil Silverman and refined by Kit Woolsey and Steve Robinson in 1977-78
If you can locate copies of the April 1977 and April 1978 editions of The Bridge World magazine that might have more details on the history of the system.
As to why it's called puppet stayman, this page has an answer from the editor of The Bridge World:
In The Bridge World's terminology, a puppet is a transfer that systemically requires partner to make the cheapest bid. Puppet Stayman is so-called because in the original version a 2♣ response to 1NT required opener to bid 2♦ (as in Gladiator before it).