Shards of Narsil
 

Why were the pieces of Ellendils sword called the Shards of Narsil, when Aragorns sword was called Anduril?

And the salute of Gondor was the moving of the hand from the face to the chest right.

Narsil was the name of the sword of Elendil, the father of Isildur. The sword was broken in the Battle on the slopes of Mount Doom at the end of the Second Age. All that remained of the sword were shards, the Shards of Narsil.

In the Third Age the shards were kept in Rivendell and a couple of days before the Fellowship set out from Rivendell the elves reforged the sword. Aragorn then renamed it Anduril, which means Flame of the West.

OK thank you that cleared things up in my head.

In the books, Aragorn carried the shards of Narsil in place of (or as well as?) a complete sword. He showed them to Sam when he met the hobbits in the Prancing Pony.