- Not available on that edition (the reason is in the tooltip)
- Depends on the setting, your class or another addon (details in the tooltip)
What it does
Checks if your current pet has exactly the name you enter. With no pet out, it does not match.
Why you might use it
Check that a particular pet is out, by its name. A Hunter who keeps a tanking pet for solo play and a damage pet for groups can use it as a switch condition, or to enable pet commands that only suit one of them. On Retail and Forever your own pet's name stays readable, because it is player-controlled. See also Have Pet.
Example
you have a pet named Fluffy
Settings
What each setting in the condition editor means, from the game's own help.
Name - The name of the pet you have summoned.