The best know hosted Fossil service is https://chiselapp.com/

Yeah, museum sounds like dead and rot… However on my small site [1] that’s the name of the fossil repos page

[1]: https://hdrz.cc/museum

> what fossils are stored in within a museum is referred to as a "repository"

I own a cute domain for that: repositoryum.com. I had the plans for it, but it's one of those that never came to a realization.