St. Louis (NA), in the standard short-form identification used for American baseball teams generally (which is "Team City (League)"), would be the standard identification for St. Louis baseball teams in the National Association (NA; full name National Association of Professional Base Ball Players).
There were two such teams, a very short-lived one in 1875 and another which (in the opinion of some sources) was a precursor to the modern St. Louis Cardinals. Because both clubs existed in 1875, and both were members of the National Association, the denotation "St. Louis (NA)" can be ambiguous and is generally avoided, and both contemporary and later records handled this ambiguity in various ways.
One club is now commonly called "Brown Stockings" but that name, though used at the time, was not then clearly or definitely established. The Red Stocking Baseball Club of St. Louis, however, carried that as their official name; they called their field Red Stocking Park and their uniforms bore an image of a red stocking on the chest.