Currently, Canvas does not automatically update group names in Canvas group activities. If you have a group activity, like a group assignment and you change the name of the group, Canvas still displays the old group name in the activity and the syllabus schedule.
Unfortunately, this problem "is not considered a bug to fix this behavior in the user interface" according to Canvas Support.
Here is a group with its original name "Test Group Original"
Here is an assignment that has been set to that "Test Group Original"
Now, the name of the group is changed from "Test Group Original" to "Test Group Updated"
Unfortunately, the students do not see the name updated, nor does the Assignment view show the updated group name. It still shows as "Test Group Original". The only way to fix the problem is to re-save the assignment. Then the Canvas Assignment will update properly to "Test Group Updated".
Canvas should automatically update the Group names anywhere they are shown in Canvas or the students get confused about who is supposed to do what and why old group names still appear in the course.