Some gods of Mycenaean Greece had similar names to those that came after at least to the best of our knowledge of Linear B, their written language, and rough depictions. But to call them the same gods would be inaccurate. The Iliad and the Odyssey in actuality represent the Archaic period which is around the 8th century when Homer lived. Their might be a vague resemblance between some gods like Demeter and Poseidon with the Greeks of Mycenaean Greece but in general these are very different cultures which did not even speak the same language. Basically Homer transposed his contemporary times on Mycenaean Greece.

This is also evident in the political, military, and geographic parts of the Iliad and the Odyssey.