Attachment
The team "GUST" is an obvious reference to Gust Co. Ltd., the company that made the Japanese version of the game. This is also prevalent towards the fact that there are logos on the machines that read "Atelier Marie" for lead pilot "Vendaval Este" and "Atelier Elie" for second pilot "Avis Rapax" and that the main colour scheme is represented for their respected games.
Contributed by Rovenami
Attachment
While not much information is given surrounding the in-game team origins, it's likely that one of the teams, Weimar, has German origins, as the team's name is a reference to German history.

The team is likely named after the Weimar Republic that ruled Germany from 1919 to 1933. Looking closely at the team's logo, it's possible to see the words "von Weimar since 2033", which is approximately 100 years after the failure of the Weimar Republic, prior to the rule of Nazi-Germany and World War II.
Contributed by Rovenami