[Overtaxed]

From Encyclopedia of Arda

Aragorn I: The heir of Aravir, who ruled as fifth Chieftain of the Dúnedain for just eight short years. He met an untimely end as the prey of wild wolves, and was succeeded by his son Araglas.

So if he were a "Chieftain" and not an official "king" and ruled for only 8 years, the Gondor folk might not have heard about him.

[carton253]

In the movie, I think for the sake of time... Arwen tells the audience who Aragorn is, the love story is introduced, then Legolas carries Aragorn's identification forward into the Council of Elrond.

In the book, the identifying mark is the sword that has been broken and now been reforged. In the book, Aragorn wants to go to Gondor to deliver the city by this sword since he thinks the dream that Boromir/Faramir had was a sign for him to claim his throne.

In the book, that sword is a powerful sign and only the king of Gondor could carry it.