12 months ago:
I most commonly see "Jasper", "Jiper" and "Jasiper" on tumblr etc.
Personally, although "Jasper" looks better and (possibly) sounds better than "Jiper", it is a common guy's name, so it's probably not a good idea. Also, how would you pronounce it? "Jace-par", seeing as the "Jas" part is meant to be from "Jason"? Pronouncing it as how you would normally pronounce it would, "Jass-par" make no sense at all.
I haven't seen "Jasiper" as much as the other two, but I think it might be a bit hard to pronounce.