In Super Mario Wonder, who is the small green caterpillar creature that travels with you, sits on your head, and equips badges? Does it have a name?
The character is Prince Florian, ruler of the Flower Kingdom, the primary location of the game's worlds.
He acts as a narrator and character being able to talk for and with both the player as well as other characters in the game. In addition, he's also enabling Mario and his friends to equip and use Flower Badges modifying or completely changing Mario's behavior and abilities, e.g. giving him different jumps, changing his run speed, spawning extra blocks, etc.