His Muslim father is also Barack Obama which means something in Muslim, I would say it has Muslim written all over it.
Then it's his birth name, and not a taken muslim name. In that case, Iam1ru1-2 is way off base asking why he kept his muslim name. Casius Clay became Muhamed Ali when he became a muslim. If Ali renounces Islam, I would expect Ali to take back his birth name. Obama is obviously using his birth name, and I dont' think anyone would really argue against that.
btw, Muslim is not a language. Nothing means anything in Muslim [sic].