Jack-a-dreams, Jack-a-Lent, Jack-a-napes, Jack-go-to-bed-at-noon, Jack Ketch, Jack-pudding, Jack Tar, Jack Sauce, Jumping Jack, Union Jack, Jack Sprat, Jack o' Lantern, Jumping Jack Flash, Jack Frost, Jack i' th' Green, every man Jack of them, Jack-slave, Jack Straw, Jack-in-office, Jack of all trades, Jack and Jill, Jack the Giant Killer, Jack of Diamonds, Little
I'm not sure you answered my question. I was asking why the small item being popped out was so called "jack" rather than other given names such as john, david, paul...etc. ?
You wrote, "It's always jack, Jack."
What about "GI Joe"? You don't say "GI Jack", do you?
What about "Uncle Sam"? You don't say "Uncle Jack", do you?
"Jack' is certainly a long-standing and traditional way of referring to the common man. We still see it today on such terms as lumberjack, steeplejack, every man-jack in the navy. It doesn't surprise me that it's 'Jack in the Box' rather than 'Clive in the Box'. Such things come about for traditional and/or historical reasons.
"Jack" for "something that jumps up" occurs both in the old slang term for ***** (cf. "jack off") and the word for the small part in a harpsichord that holds the plectrum. Shakespeare combines the two thoughts in sonnet 128:
How oft when thou (my music) music play'st, Upon that blessèd wood whose motion sounds With thy sweet