That is the question that I have heard along with the question 'How do I get pets?' and 'How do I get gold?' No worries guys I'll take care of that so I dont hear it as much :)
Well to start off, to get gold, you have to either do quests (gold and accessories as a reward ) or fight enemies and bosses ( also cool drops too ) And to get even MORE gold, just go to the shopping district and to one of the shops. And in there, you can sell the things you no longer need or want. In return you will get gold.
Secondly, to get pets you need to get gold (just like I told you above ) . Then, you go to the shopping district and go to the pet shop. (You can find it by looking for the shop that has a pig sign, or by going to your map )
Thirdly, To rename your pet all you need is 500 gold and directions to go to the dye shop. There,
click your pet icon and go to 'coat of many colors' . There just go to the bottom left and click the icon that says ' rename pet '. Then the name decisioning is up to you :)
Have fun and I hope I helped.