"Mesopotamian religion" is a convenience, and it conceals more than most such labels. The region between the Tigris and the Euphrates was not a single polity for most of its history, and the span usually covered runs from the fourth millennium BCE into the first century CE, a longer stretch than separates the present day from the founding of Rome.
The peoples and languages changed. Sumerian was spoken in the south in the third millennium and survived for two thousand years afterwards as a learned and liturgical language, much as Latin later did. Akkadian, a Semitic language, became the vernacular and divided into Babylonian and Assyrian dialects. Amorites, Kassites, Arameans and Chaldeans entered the picture at different points, each bringing gods and absorbing others.
The gods changed with them, mostly by equation rather than replacement. Sumerian Inanna and Akkadian Ishtar were treated as one goddess; Utu and Shamash, Nanna and Sin, Enki and Ea were paired in the same way. Scribes compiled long god-lists precisely to keep these correspondences straight, which is evidence of continuity and of confusion at once.
Rank followed politics. In the older Sumerian arrangement An held nominal seniority while Enlil of Nippur exercised effective authority. Marduk of Babylon, a minor figure in early material, became head of the pantheon as Babylon became the dominant power. Assyria promoted Ashur on the same principle, in at least one case by reworking a Babylonian composition to substitute its own god for Marduk.
The practical consequence is that any single pantheon presented as the Mesopotamian one is a snapshot of a particular city in a particular century. Read backwards over the whole period, it describes a religion that never existed.