What is the name of the Earth King's pet bear?

The Earth King's pet bear is Bosco.

Bosco belongs to Earth King Kuei Hou-Ting, the ruler of the Earth Kingdom in Avatar: The Last Airbender. He appears during the Ba Sing Se storyline, where the Earth King is initially isolated from the realities of the Hundred Year War because his chancellor conceals the conflict from him.

Bosco is unusual in the Avatar world because he is a normal, non-hybridized bear. Most animals in the setting combine traits from multiple real-world species, such as Appa, the flying bison, and Momo, the winged lemur. Bosco therefore stands out as one of the series' rare examples of an ordinary animal.

After Kuei learns the truth about the war and joins forces with Team Avatar, he leaves the palace to travel with Bosco. The bear is sometimes confused with other animal companions in the franchise, including Aang's Momo, Zuko's dragon-like companions in later stories, or Pabu from The Legend of Korra. Bosco is specifically the Earth King's companion and later travels with him beyond Ba Sing Se.