The name is that of the chief character in the play, Paul Pry, written in 1825 by John Poole.
He was such a perfect exemplar of those who go through life spying and eavesdropping into the affairs of others that the name was speedily adopted into the language.
Brewer’s Handbook (edition of 1898) thus defines the character:
“an idle, inquisitive, meddlesome fellow, who has no occupation of his own, and is for ever poking his nose into other people’s affairs. He always comes in with the apology, ‘I hope I don’t intrude.'”