He actually told an elderly Jewish veteran once that his name was related to one in Hebrew, which could be seen as a "Jewish name". Honestly, a lot of people walk around with Hebrew names and don't realize it, until they realize that their names are Biblical (Adam, Sarah, Jacob, etc.).
Obama's is more unique and what he's claiming is that it derives from one that historically only the Jews used, Baruch. Barack and Baruch do have similarities, especially since the /ch/ in Baruch is a sound not utilized in the English language and at times can be approximated to a /k/ sound (kh is another way to write it). Baruch means 'blessed' in Hebrew. However, given his father's Muslim background, it's probably more closely related to something like Mubarak, which has the same Semitic root of B-R-K.
The funny thing is that Barack is a given name, not just a surname, in Hebrew. It means "lightning", which to some people might be very descriptive. But that's not where his name derives from, at least according to him.