Longhouse religion is a syncretism of traditional Iroquois religion (which could probably be safely called Orenda) and Christianity. Personally, I'm not a big fan of including post religions like Longhouse or Bahá'í, unless we see a huge improvement to religion in a future expansion which brings in reformations and schisms and the like.What about Wakan Tanka, Midewiwin, or Longhouse?
This is another reason I'm in favor of treating older polytheistic religions as pantheon beliefs: they had no particular name because they were just assumed to belong to their parent civilization with very little interest in converts. Ancient Egyptians didn't even believe non-Egyptians had souls or went to the same afterlife as Egyptians until the late New Kingdom, when they were forced to reassess by having foreigners in their empire. Post-Sumerian Mesopotamians had a common stock of gods and a general acceptance that Marduk was the most important, but most people were still henotheists who chiefly worshiped the god of their city. In the context of the other religions included in Civ6 and especially in the context of religious victory, these beliefs make much more sense to me as pantheon beliefs than religions.Also, what about "Code of Laws" as the name for the Mesopotamian religion?
(To more directly answer your question, though, if I were to anachronistically attach a name to Babylonian religion I'd probably call it Enlilism, Mardukism, or Ashurism, depending on the era--Sumer, Babylon, or Assyria.)