At the end of the side quest, Hogwarts Legacy will often give you choices via dialogue. Here's what you'll get depending on what you choose.
Should you free Penny the House-Elf from Hogwarts Legacy?
Return to your newly purchased shop and talk to Penny. You may choose to either say No need Penny. I am freeing you, or That's good to hear. The first option will make Penny a free House-Elf.
Penny will thank you very profusely and wear the hat that you give her with her freedom in this situation. However, she will still choose to remain and maintain the shop if you do not free her.
What name should you choose for the Hogwarts Legacy shop?
Penny's fate will be decided on in three ways. Vesters and Venum, Cladwell and Brewsters, or Stitches and Draughts, you can do the rest. The decision will change the outside of the shop after you've made your choice, but it will have no bearing on the shop itself.
No matter how you choose to refer to Penny's status or the shop's name, you'll be able to sell unwanted items here for a ten percent discount. That's a tiny margin for the amount of pain you went through granting Fastido and Canssandra.
Do you want more help with Hogwarts Legacy? Check out Does Ravenclaw have fewer quests than the other houses in Hogwarts Legacy? here at Pro Game Guides.