It seems to be a female given name from Nigeria, in the language of the Yoruba. Various websites give a meaning of "the child is loved" or similar, including this one which seems to be Nigerian or at least managed by Nigerians:
http://www.onlinenigeria.com/nigeriannames/ad.asp?blurb=2802
Verifying this however is difficult. By playing around with this Yoruba dictionary here:
http://www.yorubadictionary.com/I saw that a word for "child" in Yoruba is "omo". Not too far away from the middle part of Jumoke, but what do I really know about Yoruba :)
Rene www.BabyNames.ch