Brand matters a lot in the ecommerce world, as we've seen with the acquisitions of Zappos, Chewy, Bonobos and a long list of others over the years. If you aren't optimizing for customer loyalty, which is usually cheaper than customer acquisition, you're leaving money on the table and eliminating any competitive advantage.
I get the impression that Bonobos had a unique product, and Zappos excelled in customer service(and i think they also cracked the formula of their market). Brand was a nice side-effect of that.
But i don't understand what brand does a store that sells similar stuff to what you can find on Amazon can get.
Zappos started out dropshipping too. The brand is associated with the curation. You'd be surprised how little others care to comparison shop once they're ready to make a purchase. As long as you seem trustworthy and your prices seem reasonable (or aren't very high in general). Once you've made them a happy customer, they're more likely to buy again if they're on your newsletter or being retargeted. It works for us and it seems to be working well for others like Wish.com[0].
What is this "brand" that you speak of ? do consumers even care ?