Various products under same store name

I have an existing store selling FBA products, I want to add some print on demand products, obviously I don’t want a second store. All of these products are my own design. Would there be any conflict if my print on demand products don’t have the existing brand name anywhere on it? Or was showing products with the brand name just one step in acquiring the Amazon brand and then they don’t really bother with it again, as long as those products don’t below to other sellers?