Before you go to that trouble, the answer is that of course it was not called French's Division Hospital in February 1863. Consider the work involved in preparing CSRs. Officers at the U.S. War Department reviewing records of Confederate hospitals apparently decided to use one name for each set of hospital rolls. That's the information which you see in print at the top of each card. Clerks then filled in the card with information from each entry on dated hospital rolls.

Another instance of this involves 1st Mississippi Hospital, Jackson MS. Obviously this hospital had to be relocated once Federal forces occupied the city. Personnel removed to Shelby Springs AL and set up operations there, but cards still read, 1st Mississippi Hospital, Jackson MS. This happened frequently as Confederate hospitals were forced to move from one point to another. Depending on the hospital records being transcribed, the U.S. War Department may have decided to save time and money by printing one set of cards.