JabRef 4.0-dev
Linux 4.4.0-92-generic amd64
Java 1.8.0_131

Steps to reproduce:

0. Open group interface. (Groups -> toggle groups interface)
1. Create a group
2. Add an item to the group
3. Right click on the group in the group interface -> edit group
4. Change the group name

Group name in the interface stays the same. If you check the group name by selecting an item and going to its Bibtex source you can see the change there.