Planets were occasionally identified with gods for the sake of poetic metaphor, but that's a specifically poetic kind of imagery. They weren't literally identified. The names are just that, names.

They're adaptations from Greek names, which are in turn adaptations from Babylonian practice. Babylonian astronomy effectively gave the planets two names: (1) an actual name, and (2) an association with a god. It's the divine names that got borrowed.

The equivalences between pantheons aren't consistent, and there was some variation: for example in Greek, Venus could be called either 'the star of Aphrodite' or 'the star of Hera', both corresponding to Ishtar in the Babylonian naming system. When the names got borrowed into Latin, the bit about 'the star of' was usually dropped.

I gave a fuller answer on this a couple of years ago, though I'm quite certain there's still more to add.

By the way, there's no consistency about believing the planets were 'holes' in spheres. I can't name a source off the top of my head that makes that claim, in fact; if you've seen one, do share it! The more normal explanaitons are that they're stones analogous to meteorites, or other kinds of objects attached to the celestial spheres. Lucian's satirical True history treats them as bodies that can be visited, colonised, and inhabited, perhaps analogous to islands: he depicts a war between the inhabitants of the sun and moon over who gets colonisation rights to Venus.