Hi David,
First of all (also in response to some other coments here) some words about coat of arms in Germany. In historic times coat of armes were granted by high autoritys (kings or the emperor) to specific people that earned it. It then became inheritable through the direct male line and always was linked to the family name. Daughters could use it, but not pass it along. People with only the same family name that are not connected through direct male line with the recipient are not allowed to use it. So if you can build a sourced connection to one of the recipients (in this case three persons) you are free to go, otherwise you can do it as well but it wouldn'd be "legitimate".
Now to your special case. The Trainer family in Regensburg was a rich merchant family with a lot of influence. Wolf Trainer was the secretary of emperor Maximilian, I think. So it is not surprising that he, his brother Achatz and his uncle Johann (Hans) got promoted to nobility and granted with a coat of arms. The family later spread to other trading cities as Nürnberg, Augsburg and Freiberg in Saxony. Their coat of armes was a Wolf in a white jacket standing to the right with open mouth on a red shield. The heraldic blanket also was red and white.
You can find a picture in the "Siebmacher" heraldic book from 1769 under the families of Nürnberg. The same coat of armes was used by the familiy branch in Freiberg, Saxony where the descandants of Johann Trainer lived as "Silberbrenner" (refiner of silver), high ranked officials under the Elector of Saxony, who were responsible for guaranteeing the purity of the silver that came from the mines and got minted into coins. This branch belongs to my own ancestry by the way, though not in direct male line. Here is a link to the "Siebmacher".
Trainer coat of armes (Nürnberg)
Hope it helps and answers your question. What I do not know for sure is the meaning of the Wolf in the white jacket. Of course the Wolf surely refers to the name of the main recipient Wolf Trainer (short for Wolfgang), but the white jacket will always be a mystery ;)