What is the name of the prince Ariel marries?

The prince Ariel marries in The Little Mermaid is Prince Eric.

Eric is the human prince who first encounters Ariel after a storm wrecks his ship. Ariel rescues him from drowning and sings to him before disappearing, leaving Eric determined to find the mysterious girl whose voice he remembers. After Ariel trades her voice to Ursula for human legs, Eric brings her to his palace and gradually develops feelings for her, without initially realizing that she saved his life.

Ursula later disguises herself as Vanessa and uses Ariel’s stolen voice to hypnotize Eric. Ariel and her friends interrupt the attempted wedding, restoring Ariel’s voice and breaking Ursula’s spell. Eric then recognizes Ariel, helps defeat Ursula, and ultimately marries her after King Triton transforms Ariel permanently into a human.

Eric is not Prince Philip, who belongs to Sleeping Beauty, nor Prince Charming, a title used in other fairy tales and Disney stories. Aladdin is a streetwise hero and later prince in a different Disney film. In the 1989 movie, Prince Eric is the single canonical answer.