There is a Boren family website,
www.boren.orgA lot of Borens who have signed the guestbook there think that they descend from the Irish Borans. There is also an implied connection with the Swedish place-name Borensberg.
On the ancestry.com website it's given as Swedish or Czech. Quite a mixed bag, and all guesses in my opinion. I reckon the jury's still out on this one.