Is there a definitive way to identify sex toy materials at home?

Plastics are outside of my wheelhouse, but I'd recommend doing a Google scholar search for "characterization of unknown plastic or polymer" and see if anything comes up. How accurate you're wanting to get is going to change the feasibility of being able to do it at home.

Off the top of my head, if you have a kitchen scale and a method to measure volume (water displacement works for weird geometries) you can get a rough density of the material and compare it to literature. Though, this won't work if it has a different material, like metal for structure, in its core. But again, I don't work with plastics so I'm not even sure if the densities of different plastics are that significant.

Hope this was helpful at all. Be safe!