From the Super Mario Wiki
The Mushroom Genie
in Mario Party 3
The Mushroom Genie, also known as the Genie of the Lamp, is a magical entity first appearing in Mario Party 2. When a player rubs a Magic Lamp, the Mushroom Genie appears and takes them to the board host, from whom a star can be purchased. It reappears in Mario Party 3, and also has a counterpart in this game: the female Mushroom Jeanie of the Lucky Lamp, who will instead change the star's location.
In Mario Party 4, the Genie is much larger and fatter than its previous incarnation. Unlike in previous games, the Mushroom Genie does not have the player ride on its back to the star. Instead, it simply jumps and lands, causing a huge rumble that sends a player to the star. In Mario Party 5 and onward, the Mushroom Genie is absent, his role replaced by the Flutter Orb.
The Mushroom Genie makes a small appearance in issue 27 of Super Mario-Kun. After getting attacked by a Thwomp, Mario rubs a Magic Lamp. Here, the genie is seen carrying Mario, Luigi, Yoshi, and Wario from falling to an evil face.
Name in other languages
Ranpu no Majin
Lamp Genie (Mario Party 4)