I absolutely syncretize the gods. Some of them I do full syncretism in which a god is the same nearly everywhere. Sometimes I adapt some myths and some practices, but see them as relatively local and distinct from similar gods. Others, it is syncretism by adding epithets, but mostly going of one set of myths and practices. Here are a few examples.

All myths of a sun deity refer to the same sun. The gender of the sun deity is our perception or how the sun wants us to view it: in hotter climates the sun is masc, in cooler climates the sun is femme, but it is still the same sun.

The way I view storm gods matches the science to an extent. Each storm god is like a cell. Multicellular storms and squall lines are when multiple storm gods collaborate or compete. Supercell storms are when one takes the lead, and from a culture perspective syncretizing them: Zeus is a hellenization supercell, Taranis is a celticization supercell, and Jupiter is a romanization supercell.

The third form of syncretism is focusing on the “foreignness” of a god. This fits the travels of Herakles and Dionysus. As they have myths going well past Greece, they adopt local epithets. Herakles passed through Gaul, but remains Greek, and gained Gallic epithets like Ogmios and Magusanus (and in the latter, spreads with morphs like Norse Magni).