"After leaving St. Louis we were advised by our guide to form a regular military organization, with a captain, to be elected by the members, to whom should be given sole authority to manage our affairs, and, in cases of necessity, ensure united action. This was agreed to, and each member of the party bound himself by a solemn obligation to obey, at all times, the orders of their captain, or, in the event of refusal, to leave the company at once. This arrangement was to remain in force for two years, or for the period of our expected absence. Tyranny, partiality, incompetency, or other improper conduct on the part of the captain, was to be punished by deposing him from his office, if a majority of the company desired his dismissal. All this being arranged, and a set of laws framed, by which the conduct of the members was to be regulated, the election was held, and resulted in choosing me as their leader."
They left St. Louis on the 19th of May, 1817. AFTER leaving St. Louis is when they decided to elect a captain, which means that until then they were a nameless group of gentlemen, just as those in the article are called (those in St. Louis just before then, in the winter of 1816). The Beale Party was not called the Beale Party while they were in St. Louis. They were just 'some gentlemen.' And they were headed for Santa Fe.