You could register your new business name as a DBA with your state. Paul’s Leather doing business as (DBA) “Super Fine Handbag Boutique”.
DBA registration isn’t usually expensive and would allow you to use your new name as a business name instead of a just a product name.
Check with your state for their rules about registering and operating under DBA’s.
If your idea becomes successful then you can always formalize it with its own business structure, trademarks, etc..
Good Luck!