In the books, Aragorn reforges the sword Narsil in Rivendell. He named the remade sword "Anduril". He carries the sword throughout the Quest of the Ring, even in battles such as in Amon Hen, Helm's Deep, Minas Tirith, and at the Black Gate. In the movies, why didn't he just reforge it in Rivendell like he did in the book? Instead of using Anduril, he used his ranger sword.
Anduril is forged by the Elves of Rivendell from the shards of Narsil at no point is it ever suggested that Aragorn had either the skill or the wish to reforge the Sword of Kings. Aragorn only takes up the sword under sufferance when it becomes clear that someone must take up the mantle of King of Gondor. I thought Anduril was brought to Aragorn at the fords of Isen, along with his banner, in The Two Towers, the wiki says he had it when he first visits Rohan but I'm going to have to reread the books to be confident one way or the other on that timing, because I thought the Elves made the decision to forge Anduril after Aragorn left Rivendell.