It is a senior monk robe. It is worn by master airbenders, and are often longer than normal robes. They come in shades of brown and orange, as well as saffron yellow.
The necklace has no specific name, but it is worn by monks. The design and carving on the wood depends on how high the monk is in the High Monk Council, as well as with their level of mastery over airbending. In Aang's case, he wore a necklace almost identical to Gyatso's, which means that he is a master airbender of similar level to Gyatso, or now has acquired the same amount of power Gyatso had in the past.
The Nomad clothing is saffron yellow, orange and brown to represent the roots of airbending.