Yeah… except no - nothing at all provided in Lemmy restricts users on that instance from trolling you in your DMs, and in posts in communities located on other instances.
You either have to block each user account one by one (and keep repeating that as new ones pop up), or else switch to PieFed to gain the ability to apply a true instance block affecting all users on it at once.
In fact I hear that lately PieFed.social even applies a user-level instance block against Lemmy.ml by default for all new joiners. It is easily removable and a DM sent to the user explaining how. The feature is transparent as a bag of rocks - I cannot even find solid confirmation that it actually exists - but aside from that it’s a good step IMHO to protect the reputation of the Threadiverse from exactly OP’s scenario.