The Name "Al Qaida"

The name "Al Qaida" means "the Base" in Arabic. This name was created by western intelligence to describe a loose organization that they, at the time, knew very little about. These people did not call themselves Al Qaida, even then. The U.S., Britain, etc. named them "Al Qaida". The name has no signifigance in Islam or Islamic teaching, so why would a group call themselves a name invented by their enemies? Why would a group called Tawhid and Jihad (Monotheism and Jihad) change their name to "Al Qaida in the Land of the Two Rivers", then suddenly promote attacking Shiites? Its like mujahideen calling themselves Islamists or Jihadis. These are names created by "westerners" to describe and defame the mujahideen. No real mujahid would call himself a "jihadi" or an "Islamist". It has no signifigance and is not a word in the Islamic or Arabic vocabulary.