From the Super Mario Wiki
The Toad Professor is a character in Paper Mario: Color Splash. He is a yellow Toad, and he owns a pet Chain Chomp named Princess. When Mario and Huey go to his house in Château Chanterelle, they are told by a Toad that the Professor is taking a walk with Princess in Mondo Woods. The Toad Professor can be found at the end of Mondo Woods, crying on top of a Giant Brick Block because he lost Princess. Huey tells the Professor that Princess probably went back to Château Chanterelle, and the Professor heads back there with raised spirits. However, when Mario and Huey arrive at Château Chanterelle, they find the Toad Professor crying on the ground due to Princess not being there. The Professor gives Mario an Excavation Site Permit so that he can explore Marmalade Valley.
After Mario finds the Bone in Marmalade Valley, he can take it to Château Chanterelle, which causes Princess to return briefly. She jumps and rolls on the Professor, and his assistant worries that he was crushed. The Toad Professor, however, becomes happy, and tells Mario to give Princess another Bone if he finds her again. He will then give Mario a Sharp Spike as a reward for finding Princess.