In the case of Germany, I am sure the Pivi is right. I can’t speak for other countries as the name “Parabellum” connected to the two calibers 7.65 and 9 mm would have been a “pass me down” from DWM’s usage, and could be interpreted in those other countries as they pleased - that is, it could have been used for a military designation. However, in Germany, I believe it was primarily a commercial appellation. As we know, the 9 mm was, for German military service, the Patrone 04 (German Navy) or the Patrone 08 (German Army, and eventually the usage by all services). That is not to say that no military document, manual, etc. ever used the word “Parabellum.” I simply don’t know. But, it was not the standard military terminology. Since to my knowledge, Germany never officially adopted the 7.65 mm Para, it could have been listed in some official military or police sources using the commercial “Parabellum” designation - again, I just don’t know. I don’t recall ever seeing it referred to in a military document, but it almost must have been at one time or another.
Oddly, there was a Polte nickeled dummy of the standard Exerzierpatrone type, with no actual primer but rather just a dimply for firing pin clearance and with an “Ex” headstamp, made in the 1920s. I don’t know for what reason this was made. Perhaps EOD or Peelen or one of our other German friends knows why or for whom it was made?