Arabs thought that Allah is the supreme God. The Jews and Christians thought Jehovah is the supreme God. So when these two groups communicated they assumed they are speaking of the same entity. Indeed they did because by these names they intended the same thing just as when you say Sun or Shams you are talking of the same star in two different languages.  

However, originally Allah and Jehovah were not one and the same deities. Both these deities are figments of human imagination. As these imaginations evolved the concept of these gods also evolved and when both groups, i.e. the Jews and Arabs adopted monotheism, these two gods merged and became two names of the same God.  

In fact Elohim and Jehovah are mentioned in the Bible as two names of the same God. However, originally these were two distinct gods. One was the god of the Judea and the other was the god of the Israelites. When these two tribes merged to form one single nation of Jews they also merged their sacred books and their gods into one single God.    

The concept of God is entirely manmade. It evolved as humans evolved. Allah, Jehovah and Elohim were originally distinct gods each with their own limited purviews. As the idea of God evolved and monotheism became the vogue, there was no room for different gods and hence all these gods merged to form one single deity and the names became interchangeable. They only exist in human imagination. At one time they were distinct deities and now they are one and the same.