We know that "The Rains of Castamere" is identified as "The Lannisters Song".
Do other Houses (e.g. House Stark, House Targaryen, etc) in A Song of Ice and Fire and Game of Thrones have a song that is identified with them?
As Kris says, "The Rains of Castamere" is not an official song as their sigil or motto is official. There is no official anthem/songs related to any House. Still, we can do a list of songs more or less related to a house or a character: