It's a mere convenience for you.
Otherwise u can always rename a restaurant u frequent as office supply store
The way they will assign which purchase is 5x, 2x, or 1x is by how the merchant has classified itself as a business (entity) and how it's processeed.
Example, I have purchased something from H.com because they were having a promotional 5% cash back instead of 1% for online purchases.
Even though it went through H website perfectly, it was run through as a phone order so guess what, 1% for me.
Same with a grocery store that has a Starbucks inside. Even though it's a Starbucks, it's running off of the grocery store's payment processing system. If I had a card that pays more with grocery purchases I can easily rack up a lot of points..Amex has a card for this.
In your online account, when you click the item you should see additional information. That should give a clue as to how it's perceived and the amount of cash back you get.
You can label it any way you like, it's only for your convenience and will not influence or impact how you earn the rewards.