[Finwe]

I don't think you're giving Sauron the credit that he deserves. The guy was bloody brilliant. He knew enough about the Elves, their private squabbles, and their motivations to ingratiate himself with the Gwaith-i-Mirdain. According to some sources, Celebrimbor (or Enerdhil) made the Elessar in Gondolin, and gave it to Idril to heal the hurts of the world. She then passed it on to Earendil, who bore it when he sailed West. Then, in the Second Age, Celebrimbor made another one to proclaim his love for Galadriel. That is the one that she passed to Arwen, and which passed to Aragorn. If Celebrimbor had indeed made an Elessar, then it makes sense that he would have told Annatar about it, since the two were "comrades-in-arms" so to speak.

By the time that the War of the Ring was underway, it was revealed that Aragorn was the Heir of Isildur. His spies would have brought him the news that the people of Gondor were calling him Elessar. Sauron would have naturally put two and two together, and realized that he could use Aragorn's desire to rightfully become King to his advantage, and try to demean him.