What's the point of publishing your peer review report along with your new paper?
Are their names known in advance, during review, before the paper is accepted or rejected?

Depends on the journal. At Nature family journals, I believe the identity of reviewers that choose to sign their reviews is only revealed at publication time.

Why does the author choose to publish the peer review report of their new paper?

I imagine it is because they are primarily supporters of the concept of openess in peer review. I pass no judgement on the merits either way here, but you can't be a supporter of the theory of open review (and therefore gain its benefits - like more reluctance of the part of the reviewers to be unfair), and then not opt to publish the reviews of your papers.
It will also help readers to have confidence that the paper has been properly reviewed.