Everyone will know the name, but not why they know it. You will then be able to ask him and other townspeople about Miraak. Upon arriving on the islands port town of Raven Rock, a Dark Elf by the name of Adril Arano who will ask as to your intentions of arriving at Raven Rock. You can either persuade him, intimidate him, or bribe to get him to take you to Solstheim. Travel to the Windhelm docks to find a boat with a Nord named Gjalund Salt-Sage, and listen to his conversation about how he doesn't remember the cultists forcing him to sail to Windhelm, and how he's too creeped out to go back. Search the bodies for a letter detailing the cultists plan to set sail from Solstheim to Windhelm to track you down and kill you - all for someone named Miraak.
If you would rather let someone else do the work, lead them to any town guards who will no doubt make short work of them. The Cultists can also summon Seekers - nasty mage-like daedra that will shoot projectiles at you. You can play dumb or own up - either way they will attack you. In any case, two cultists will approach you and ask if you are the Dragonborn. You can either wait in one of the main holds, or head to Windhelm and take the boat to Solstheim yourself.