UltraCosmetics contains a feature that allows players to rename their pet. The name is stored with the system specified in Ammo System section.
The Ammo System doesn't need to be enabled! The storage system configuration is just located in Ammo System Section!

How do you use it?

To turn on this feature, just change Enabled: false to Enabled: true in the configuration file.
If Permission-Required is set to true, the permission ultracosmetics.pets.rename will be required to rename a pet.
If requires-money is set to true, it'll require the specified Price to rename a pet. See the economy page of the wiki for more information about how to select a currency.

Configuration snippet:

Pets-Rename:
  Enabled: false
  Permission-Required: false
  Requires-Money:
    Enabled: true
    Price: 100

How do you rename a pet?

You can rename a pet from the Pet Menu or by using the command: /uc menu renamepet.