In Disney's 1989 animated film The Little Mermaid, Prince Eric's dog is called Max.
Max is a large sheepdog who belongs to Prince Eric and lives aboard or near Eric's ship. He recognizes Ariel's kindness and quickly responds warmly to her, unlike Eric, who initially does not know that she rescued him. Max's reaction provides an early visual clue that Ariel is trustworthy and important to the story.
The dog appears during the film's opening ship sequence and later on the beach after Eric's rescue. Max also reacts strongly to Ursula when she arrives in disguise as Vanessa, helping create comic tension during the wedding scene.
Max is easy to confuse with other animal characters from Disney films, but he is specifically Eric's dog in The Little Mermaid. He does not speak, and his name is not connected to the human characters' titles or family names.