I had a North American man pestering me for almost a year. He used a myriad of different names, numbers and email addresses to do so but his style of communication always gave him away. I have blacklisted him everywhere I could think of, including CE even though his number is not a UK one.
I used to tell him I had no availability, but still he messaged me. In the end, I just ignored his messages, and eventually he stopped. That’s all I can really suggest you do - he will get bored once he realises you’re not going to communicate with him.
(I also had a Canadian guy harass me in a similar way. However, as I had his real details - name, ID etc, I threaten reporting him to his local chamber of commerce and police for harassment. He stopped bothering me and never contacted me again. In this instance, I was lucky to a degree as I knew who he was/that he would lose his livelihood if I made a complaint against him.)
Don’t let your anxiety get the better of you. Stay strong and ignore him. He will move onto someone else (unfortunately for them).