General Terms:
* Magician
* Birthday Magician
* Party Magician
* Entertainer
* Magic Show Performer
* Illusionist (if they do more elaborate illusions)
More Creative Options:
* The Amazing [Magician's Last Name]
* [Magician's Name] the Magician
* The Master of Magic
* The Magic Maker
* The Birthday Magic Wizard
Ultimately, the best name depends on the magician's style, the age of the birthday child, and the overall theme of the party.