In the Canvas Student app, it's easy for the students to see which canvas course each group they're a member of belongs to. But in the desktop interface, this information is not visible. We of course try to train our teachers to not use generic group names, but this is very hard to get across to thousands of teachers with varying digital skills.
My suggestion is to include the course name (or at least the SIS-ID) that each group belongs to in the groups overview.
I've attached examples of the desktop overview vs the canvas student app overview below.