Little is known about the shadowy paramilitary group which is believed to be linked to Russian oligarch Yevgeny Prigozhin, who is himself an associate of President Vladimir Putin.
The presence of Wagner paramilitaries has been documented in Libya, Mali and Syria, among many other countries, as well as in Ukraine.
Naming the group Mozart was "a tongue in cheek" retort to the group, according to Andy Bain, a former US marine reserve officer.
Mozart -- which was set up after the war started by an ex-US commander and is funded by donations -- provides military training, but Bain says what they teach is really "a lot of common sense."