Early sail numbers can be a can of worms. To understand, I guess we have to look at how they came into being. Early boats had no numbers at all. By the early 1880s some regatta fields had become too large to permit easy identification and the sail numbers were distributed prior to a race. I say distributed because they were physically distributed as a big piece of cloth with the number painted on it. This number was then sewn to the sail for the duration of the race or the cruise (as was the case in the NYYC cruise). Thus, a boat's number could easily change during a single season.
At around the turn of the century and with the arrival of one-design classes such as the Buzzards Bay 15 (which you are interested in in this case), it usually was the club which had organized the collective order of the boats which also assigned the sail numbers. Thus, Beverly Yacht Club, apparently gave the numbers to the owners of the 15s. But they were still a piece of cloth sewn to the sail. And they differed in minor details. The E in the sail numbers of the 15s, for instance, can be seen on old photos both with serifs and without. But, and this was a big change to the previous practice, these sail numbers stayed with the boat over long periods of time, usually many years.
Only with the advent of racing organizations that spanned across several clubs did sail numbers come that were centrally assigned to a boat and stayed with it for most of its life (or the duration of the class a boat raced in) and were an integral part of the sail and not just a sewn-on accessoire.