Um lets also see....The area they live in is FRENCH...Sault Ste Marie means St Mary's Rapids in french, most of the people in the area are french or italian.
The music they USUALLY play isn't usual...It changes from year to year.... I never played Scottish music while I marched there...
There is NO connection to Scottish except the kilt...and even that is an arbitrary connection...
If a scottish name is chosen, the history of the Bandettes isn't there then...sorry, but if you're going that route, why not just start something brand new.