You don't actually have to have two pets to use name tags. People do mainly use 'em for switching names from pet to pet, but you could also just change the name of one pet to a new name that's not taken yet.
And of course, if you are switching a name from one pet to another, you don't always need two tags. If the pet receiving the name is already unnamed, like if it was in your hatchery or graveyard, then you'd only need a tag to rename the pet that already has the name you're moving, to make it available again.
This is why people sometimes let pets die - to make them lose their names so a tag doesn't have to be used. But be careful when doing this. You never want to graveyard-clear a pet with a name you actually want to keep. Someone might notice your Creatu in the graveyard and take its name once it clears.