Senator Obama was reportedly named after his father, Barack Obama, Sr.

The Senator's first name, Barack, is a Swahili (Kenyan dialect) name that has its origins in the Arabic language. The original Arabic root of the name (B-R-K) means "blessed." In Arabic, the root word is used in many other phrases to denote blessings and to describe people who are blessed:

Mabruk! = "Congratulations!"
Barakallah feek = "May God bless you"
Barakah = blessings from God (feminine version of the name)