It is a name, they usually don't get it from their parents, but from the government. Because they are very special and shouldn't be seen on the same niveau as most people.
Slice of Life. In shonen anime, an episode that does not necessarily advances the plot, but instead shows how the characters live their "normal life" when not having an adventure.
Person A: I love when they air SOL episodes of the Konoha 11!
Person B: Yes, I like to see how they interact with their families and other people of the village