Wikipedia has a nice long article about the cave, and its history going back to Herod. There's also a short discussion of how the tomb is viewed by the three major Abrahamic faiths. But it's weirdly lacking in any serious discussion of who modern scholars actually think might be buried there.

Relatedly, what's the earliest we can reliably attest that the site was revered or known by locals? Was there at that time some "tomb" already there, and if so how old is that?