A storage system has been added for your companions. They no longer take up bag or bank space. You now "learn" each pet, once you get them, similar to a spell. You can carry all of your pets around at once and summon them whenever you want. The same system is used for player mounts.
Press "Shift-P" to open up your pet menu. You will then see a list of all of the pets you have. Right click on any of your existing pets to store them. If you want to summon a pet more quickly, drag the icon to one of your action bars.