I've known quite a few, mostly English and American, and all around my age or slightly older or younger (I'm 30). Indeed most of them went by
Jenny or
Jen. The ones who went by
Jennifer were not in English-speaking countries.
I think this name will become very dated and needs a long, long rest. And even if the full form of the name isn't so common, I know all the
Jen and
Jenny are really
Jennifer, so the full form feels just as boring.