No, Christians and Jews worship Jehovah God, God Almighty. Muslims worship Allah, a 3000 year old moon god that was a local god at best. They are not the same
There is some evidence that the name Allah referred to a pre-islamic god. There is also som evidence that Jehovah or Jahveh is of Egyptian origin and also referenced a moon god. Both theories are contradicted by other evidence.
Since a good deal of Christian tradition has pagan origins including elements of the celebration of Christmas ( and I am not saying Christmas is a pagan holiday, only that some of its origins and characteristics are)I think it is shortsighted to attribute an entire belief system to the supposed origin of one word.