Zendesk Spammers

Iv’e been having an issue and was wondering if anyone has an idea. I use the zendesk chat widget on my website, and there has been someone with an unknown motive who is sending all kinds of obscene text. He uses a dynamic IP so blocking the IP won’t help. I suspect he is using a VPN or proxy or the like. Blocking the cookie doesn’t fully take care of the issue as he can just open a new browser window… Do you have an idea how to block him?