Go to the DIY shop and keep going along untilyou will get to them :)
To change your pets name in Pet society you go to the "Stylist shop" and once your in back space your characters name and type the new one. It will cost you 30 coins.
Go to the Stylist and type over the name your pet already has, then click the tick.
UH. go to stylist then choose. but wait. you must have money to Pay for the changes..
Go to the Stylist and pay 20 coins to change the gender of your pet.
Well you go to the Stylist shop and where your name is you erase it then type the new name you want , but it costs you at least 30..