[Overtaxed]

It's just my opinion, but I see Denethor as too proud to go whining about Thorongil to anybody. And Boromir doesn't seem to resent Aragorn on the journey south.

If the kings had been gone for 1000 years from Gondor, how would Boromir have recognized the name of Aragorn, son of Arathorn. Do you have any ideas?

Not unless he recognized the name "Aragorn" from one of the old kings. Isn't our Aragorn "Aragorn II." But still that old king would have been from the Northern Kingdom and I'm not sure if the Gondor folk would keep up with Northern Kingdom lineages.

[carton253]

Of course, in the book, the tell tale sign of "kingship" was the sword that had been broken. In the Council of Elrond, Aragorn showed it to Boromir and Boromir accepted it (barely).

So, now we get a clearer picture. It wasn't the name that Boromir recognized; it was the sword. That's from the book. In the movie, it was the name, since the sword is in pieces still.

[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.