In 1668 Richard Elton described this organization as the "Ancient and Honourable Artillery Company of London. This was probably one of the first times that particular label was applied to this organization. The following table lists the various names by which the organization was called before that time (during the period we are interested in.)
Note: "Artillery" at this time refers to anything that shoots including muskets. "Infantry" is a later French adaptation introduced around the begining of the seventeenth century.
From: Walker, G. Goold. The Honourable Artillery Company 1537 - 1947. Aldershot, Gale and Polden Ltd, 1954. [ page 24]