The thing is, the same gods are explicitly called different names in different Old World languages without them being different gods. Consider this:
Haendryk is known by many names in the Old World, depending on the local dialect of Old Worlder. In the Empire he is 'Handrich'; in Bretonnia 'Affairiche', in Tilea 'Mercopio', in Estalia 'O Prospero' and in Kislev 'Kalita'. His worship is not popular in Norsca (he's too much of an urban god), while the Arabyans disapprove of his association with usurers and have banned his cult. Elves and Imperial Dwarfs have no equivalent, while a few expatriate Dwarfs who live among Humans worship him in his local form.
That doesn't seem to matter though. They all know who they're worshipping.
As a side note, I saw looking for this that the Marienbergers believe that Haendryk is an ascended mortal, and some claim descent from him