Your first pet is Henrietta, but you can get other pets/companions to adventure with you. This page is all about pets.
Henrietta
You will automatically get Henrietta as your first pet at the beginning of the game.
Pet Health
Your pet's health is displayed with green hearts, above your red hearts. If a pet has at least one empty heart, it will automatically try to gather hearts that you find.
If your pet's health is too low, it will run away and hide until either all enemies are gone or until a heart appears. It will try to take the heart, but if you take the heart instead, your pet will run away again.
Calling/Sending Away
Use the pet whistle that you got at the beginning of the game to call your pet or send them away. If sent away, they will remain off screen until you use the pet whistle to call them back.
Other Pets
There are two other pets: Bruce the bat and Gourdon the pumpkin. They can be found randomly in the overworld. Check on them and say Yes to get them to follow you. Your previous pet will switch places with your new pet, but may move to a random map location later.
Bruce and Gourdon will attack nearby enemies that are within their range.
MeggaHenrietta
If you find Phoenix Ash, check on Henrietta to evolve her into MeggaHenrietta. Instead of running away from enemies, she will attack the nearest enemy on screen until none are left. Phoenix Ash can drop randomly from things like killing all enemies on screen, pushing gravestones, killing mini-dungeon bosses, etc.
Paige
After you find 8 missing library books, you can talk to Paige in the library to have her join you. She works the same way as other pets, and will throw books as projectile weapons at enemies.