Speaking as an outsider who has never been to China, I can say that if I was visiting your country and saw a store called "Number 2" it wouldn't occur to me that it was lesser than the one called "Number 1." I might think that maybe they were the second retailer to get a license or something like that, but I would not automatically assume that Number 2 sold goods that were inferior to those sold at Number 1.
In the US, it's not uncommon for many different stores or brands to boast that they're number one, so that sort of rank seems totally subjective to us. We don't place a lot of faith in such boasts, and there are a lot of folks who shop at places that don't bill themselves as number one or "the best," because they believe they'll find bargains/better prices at the "number two" store.