Yahweh is a personal name but Elohim is a title and is translated 'God' as is El-shaddai which means "God of the mountains," (according to wiki) and so is Allah..its a title and if you ask a muslim the name of their god, it doesnt have a name , they only know him as Allah.
This is all correct as to how these things are interpreted now, but that doesn't necessarily mean they all used to mean the same thing to the people of many many centuries ago. Taking Allah, for example, it's true that it just means 'The God'. However, Allah didn't appear in Arabic religion with the arrival of monotheism. In polytheistic Arab culture, Allah referred to the chief God - the creator; but he was not the only god. There were a whole host of other, subordinate, gods; including his daughters - the local deities al-Manat, al-Uzza and al-Lat.
In the same way, Yahweh may have been the chief God amongst a pantheon of lesser gods originally. The fact that the Bible shows Israelites worshipping other Gods and prophets having to convince them of monotheism would confirm this as a near certainty, in my opinion.