How does a lawyer know who to send the threatening letters to? This whole conversation exists on the assumption that you're not fully anonymous in this relationship.
You aren't fully anonymous. Privacy.com has your info. The vendor, or their bank, can easily determine you gave them a privacy.com number. A court will happily compel privacy.com to turn over your info if the vendor can show the most basics of an agreement between you and them.
It doesn't guarantee the vendor will win a final judgement but no court is going to prevent them from tracking you down.