Choose your wolf in the 'Customize Wolf' panel (available when starting new game in Amethyst Mountain, then click 'Modify', then click on your wolf's name and type the new name. Be sure to click 'Save' or 'Continue'.
To change your mate’s name, all you have to do is load a game, then click 'Player stats' and edit the name put in for your mate.
Provided you have accumulated a sufficient number of experience points, you also may be able to change your pups’ names. To do this, load up a game in Slough Creek and click 'Pack stats'.
From there, you’ll be able to modify the names of your pups after they have been born.