Brand name is what will go on your product. This is the name that customers will see and associate with your products. It's important to choose a brand name that is unique and memorable. This name can also be anything you choose, but it should ideally reflect the nature of your products or the image you want to project. For example, brand names like 'Nike', 'Lululemon', and 'Apple' are all well-known and easily recognizable.
Store name is what you can put as your "seller name" on Amazon. This is the name you use when registering to sell on Amazon. This is a back end type of representation. It can be any name you choose and it doesn't need to be your business registration name or your brand name. For example, it could be something like 'Tom's Store' or 'ABC 123'.