If you were concerned about initials, Jack Elliot W would be J.E.W. Would that be any different than NEW? Not trying to be snarky or anything, but I just wanted to point that out!
This was the first thing I thought as soon as I read the idea of Jack instead of Noah. If I had a problem with initials that spelled words (I don't, really, aside from obscenities and other negative associations), that would give me pause at least as much as the initials N.E.W.
I like Noah best of your choices, and then Jack. I don't think of Noah as young - the biblical Noah lived to be super old, so what's actually weird to me is that it's so popular for babies right now.