As AACW will organise units up to army level, it is expected that we will use the actual army names. The North tended to name their armies after names of rivers. The South named their's after states or regions. Examples are the Army of the Potomac and the Army of Northern Virginia.
However, it might be too much to expect non-native English speakers to pick up on one of the nuances of the English language.
The Union 'Army of the Mississppi' refers to the river while the Southern 'Army of Mississppi' refers to the state. The difference is the use of the article 'the'. All Union armies need to have 'the' in their titles, while Southern need to not have it in their's.
We do not have such a case as this in French. Probably the closest would be 'King of France' versus 'King of the French' which while looking similar, imply different concepts.