torchlight-2
As per this question, the only difference between companion pets is aesthetics and a special effect that occurs when you feed fish to your pet.
However, I'd still like to know is it possible to change companion pets once you have started a character, or does this involve starting a new character?
Yes it is possible, simply open up the Pet Panel (default of P) and move items from your inventory into this screen;
It is also possible to get your pet to purchase consumable items such as scrolls and potions by clicking on the 'Shopping List' option on the tabs at the bottom (first from the right);
When you're ready to send your pet back to town, click the little green house icon in the bottom right of the screen. This will change the Pet Panel screen to show how much time is left before your pet returns;
This is also detailed on your pet's health bars when the Pet Panel is closed;
Pressing Shift+Z will give your companion pet a health potion.
It is not possible to give your pet a potion when already at full health.
Giving your pet a potion will place a temporary indicator next to their health frame showing how much time is left on the currently active potion;
It is also possible to give your pet a mana potion by pressing Shift+X
Best Answer
In general, you will have to start a new character.
A second option is too hope for a fishdrop that let's you change your pet permanently. Those do exist, but are very rare and hard to come by.
I personally found one that changes the pet permanently into a spider.