Not sure about the name actually, but they do get the email address - that‘s how they were able to email me an invoice without me entering anything.
That said, my my email address does contain my name, and while I could configure an alias in my Apple Pay settings, I doubt that too many people would do so. Would be a nice way for Apple to use their email privacy relay feature.
I do not think the merchant gets a name or an email address.
https://developer.apple.com/forums/thread/715893