Max
In the directories the pub name was often not given.In a lot of cases, though I don't think all, this was when it was a beerhouse, which only had a licence to sell beer (& cider ?) , not spirits. The name often, though not always, appeared in later additions, and usually, but not necessarily always, this was the name that it had been known by before. (Sorry for all these usuallys and not always , but there seem to be cases when it can't be definitley stated) So , yes it is very possible that no 15 was a pub in 1903. I did forget to put in one extra extract though (must be old age). It was also listed as a beer retailer in 1908, but by 1912 it was described as a shop (no specific type), so , if it had been a pub earlier, this had changed by 1912.
mike