You can name your Petkin

Through their location:
> Go to the apartment your Petkin lives in,
> Tap your Petkin,
> Select Interact from the action list,
> Tap the name field to edit your Petkin’s name.

Through the Dressing Room:
> At the Dressing Room, tap your favourite Petkin,
> Open the Interact option from the action list,
> Tap the pencil icon to rename your Petkin.