I mean... I come from the forum scene and they were always called PMs, as in Private Message. What in the hell does DM stand for and when did things change from people calling them PMs to DMs.
Twitter used Direct Message instead of Private Message because they needed to establish that there is legally no understanding of privacy for DMs, because Twitter will surrender the contents of DMs to law enforcement / government / data collection. Fediverse should also use DM because there is again no guarantee of privacy (and you do not expect there to be).
Still, the conversation is private, as in not public. Even if it is surrendered to the authorities, the'll probably never be released publicly (unless leaked).