Thank you for your post!
I was able to reproduce this issue with FileMaker Pro 16.0.2 on both MacOS and the Windows Operating System. I followed these steps:
1. Created test.fmp12
2. Created two Button Bar Objects
3. Grouped the Button Bar Objects
4. Opened Layout Object Window and Renamed Individual Segments
-The Main Button Bar Object Name was changing with the last Segment Name modified
-This is not the behavior of an ungrouped Button Bar Object
I have sent a report to Testing and Development for further review. I will post back here when I receive a response.