You should put your pet in the stables and tame a different one and if you like another pet better with your pet active you can left click your pets name plate and go down to abandon pet well you can use the ability calleddismiss pet or you can just put him in the stables and go tame. How do i get pets for my hunter can i get more than one pet and if no to the last question can i get rid of a pet for a different can of pet and lastly do pets level up the same time as the person controlling them. Also if you do want to keep it but wanna get a different pet go to a stable master and put it in there and you will be able to get another. So you see other wow hunters with their pets and you dont have one or even know how to get your first pet.
Assuming you are a hunter the best way to permanently get rid of a pet is to call it so it is running with you and then right click its portrait. Dismissing a pet just puts them away for until you need them again you need to right click on thier picture and abandon to get rid of it. There are a couple different ways if you mean pet as in a companion you can buy them in your factions cities off of the auction house world drops in the wow. Obtaining a pet and taming it is one of the coolest things about being a hunter in world of warcraft.