What should I call my bakery/home cake shop?

[Lucy]

I am starting to make cakes and sweet treats from home. I want to set up a facebook page/etsy page so people can order from me but I don't know what to call it.

I'm not sure if I want to incorporate me name or not but just for reference its Lucy.

[Erin]

Sweet cakes.
Lucy sweet
Sweet nothing's
Home cakery
Sweets back home.
Sweet treat
Lucy's home shop
Lucy's bakery
Home sweet home.
Forever sweet
Sweet tooth
Sugar on top
Beloved bakery

[Piran]

Not legal in the UK Lucy. Too many food regulations. Your kitchen has to be inspected before you can trade and you need food handling certificates and Insurance. You need permission from your Council.
You need to talk this over with your parents as they are the ones that will get into trouble.
UK

[shipwreck]

Grandma Lucy's home style deserts.

That will make people think they are homemade even though you are allowed to make commercial food in a home kitchen so will never sell homemade treats.

[Dumdedum]

You cannot do it without jumping through hoops.

Registering as self employed and having Public Liability Insurance in place in case your products cause harm to other people to start with.

You will need Food Hygiene Certificate and the hardest one of all is the Environmental Health inspection of where you are intending to cook. And you will need that to be able to sell your cakes in the current climate. They like things like a second sink for hand washing and other stuff to be able to tick all the boxes.

Then choose your name.

[HuckingFilarious]

Instead of answering your question, PIRAN above has rushed to tell you that you can't open such a shop. But you didn't ask if you could open such a shop, you merely asked what to name it. Makes me wonder who is the child here, you or her?

Why don't you just call it: Luscious Lucy's Cake Shop.

[Fairdo4all]

'Day Dreams' because that is what it is. You cannot legally make and sell consumables from a domestic kitchen.