What do you think of the combo 'Eden Eloise'?

I loathe alliteration. It is very unnecessary, IMO. The whole idea surrounding it appears cheap and uninspired. It's even worse in this case because the "ee's" make an identical "ee" sound. I suggest you reconsider; keep Eloise, tho'. The name is fantastic. It's underused, cly, feminine, exotic and it will age wonderfully, whereas as Eden is a fad, trendy, silly and infantile.