How do I report multiple messages?

So I've been harassed by this guy who just wouldn't stop reaching out to me, probably some drunk a-hole who want to punch me or something but can't because I'm not actually there.

I could just block his profile and such, but if guys like him (or much worse people) starts bugging me through the internet, how do I, say, “kill” the contact between me and the multiple accounts that person might have?