One solution is to make the forum private (click on "Options > Users > Change permissions" and make sure that only members or admins can view). Then you would have to add all good users to the list of members.
If you want to keep your forum public, then the easiest solution is to keep banning the user. It is much simpler for the admin to ban the troll than for the troll to keep creating new accounts and registering to your forum. So sooner or later they will get tired and leave.
Vespert wrote
Also, can the "Send Email to <username>" function be restricted? I think they are using this function to directly spam users' personal mailboxes.
This is more complex and we don't have a solution ready for you. If we get a request at the premium support forum, we will find a solution.