It probably was but it probably wasn't available down at the corner hardware store. My (current) impression was the the boxes were more often than not marked with the gun they were supposed to be fired in rather than some technically correct designation. When did it become common, for instance, to add a metric length to a cartridge designation? That is, in this country. It was apparently the standard way of describing European made rifle ammunition at least 80 years ago, at least for German made ammunition (but not pistol ammunition). English made ammunition was not so described and the few instances where the case length was included, it was in inches.
Remember again that the "official" name of a cartridge, if there is such a thing (the subject of this thread), may not even be on the cartridge. I've already mentioned ".38 LONG" on some cartridges I have. I am led to believe the full name is ".38 Long Colt."
A quick look through one of my reference books suggests strongly that ammunition was packaged in boxes marked with the specific firearm it was intended for, even to include the model number, so confusion should have been minimal. Even so, there were a fair number of cartridges that allowed one-way interchangeability, just in case the correct one wasn't on hand.
Actually, we can't really be sure what most people really did call things 130 years ago very often. Even 50 years ago some terminology in firearms that has mostly gone out of common use.
Shoot low, sheriff. They're riding Shetlands!
Underneath the starry flag, civilize 'em with a Krag,
and return us to our own beloved homes!
Buy War Bonds.