Two names, and only one of them is held exclusively. People assume it is the other way round.
Your username is unique
This is the one in your store’s address, and no two accounts can have the same one. The screen tells you as you type: ✓ available, or That one’s taken.
So if the name you want is gone, it is gone as a username, and you need a variation.
Your store name is not
Nothing stops two stores sharing a display name. There is no uniqueness check on it, and no reservation.
That is deliberate rather than an oversight — a short, plain name is often the right one for a small store, and holding every one of them exclusively would mean a lot of stores called something awkward.
Which means two practical things
You will not be blocked. Pick the name you want and it will save.
You are not protected either. Another store can use the same display name tomorrow, and the thing separating you will be your username, your ratings and your followers.
When it stops being just a name
Using a name that somebody else has built a business and a reputation on is a different matter, and the fact that the app does not stop you does not make it allowed. The not-allowed list covers passing yourself off as someone else, and a rights holder can ask for it to come down whatever the app let you type. Using someone else’s brand, photos or words
So: a common word, fine. A name a buyer would reasonably mistake for an established brand, not fine, and the risk is yours rather than Metzee’s.
How to choose one you will not regret
Short enough to say out loud in a show. You will say it hundreds of times.
Spellable after hearing it once, because that is how people search for you again.
Not tied to one product. A store called after a single thing you sell is a store that has to rename itself the day it grows.
The same as your username if you can get it, so people typing what they heard arrive in the right place.
Changing it later
The display name can change. Your username is the one that is painful to change later, because it is the address people have saved and shared.
So spend the thought there, now, and treat the display name as the easier decision.
More: how to set up your store, how to choose a store name, what makes a store look trustworthy.