EDIT: Or maybe not so quickly. So far it's 2 votes for gill, 6 for jill, and 1 for jee. Perhaps we'll never know.
Because while a lot of sites say it's jill, I also found this one:
Dear David Letterman.
The next time Jake Gyllenhaal -- or his sister Maggie, for that matter -- is on your show, please try to pronounce his name correctly. It would mean a lot to the young actor.
"My last name simply means 'golden hall' in Swedish but it really gets butchered in English," Jake, who has appeared in "The Good Girl" and "Lovely and Amazing," told celebrity researcher Baird Jones the other night at the premiere party for "The Secretary," in which Maggie stars.
"Sometimes it just comes out funny, like when I was on David Letterman plugging my next movie, 'Moonlight Mile,' and Letterman kept calling me 'Jill-and-Ham' the whole time," he says.
Other people find a way to get 'guile' or 'jilted' in there, but Gyllenhaal would like you all to know, it's pronounced Gill-en-hall.
Are we clear now, Dave?