When we first see the Maximoff twins, introduced at the end of Captain America: The Winter Soldier, we are given the impression that they are two of the Universe’s many villains. Indeed, for most of Avengers: Age of Ultron, they fight against our heroes, using their powers to confuse and dismay the team.
However, by the end of the movie, they have joined the Avengers and are hugely instrumental in defeating Ultron. Hawkeye, in particular, witnesses the bravery of Quicksilver, or Pietro Maximoff during the battle. So when he loses his life, Hawkeye lovingly uses his name as a middle name when his son is born. It’s a touching tribute to an interesting character.