Updating resource group names

I have noticed that if I go to Resources > Groups and change a group's name, that changed group name does not reflect in any firewall rules that reference that group.

For instance, I create a group named group_1.  I create an Internet Firewall rule with group_1 as the source.  If I go back to and change the name of the group to group_one, the group name group_1 is still listed as the source in the Internet Firewall rule (it seems like it should update to group_one when he group's name is changed).

If I change a group name that is referenced in a firewall rule, do I need to manually update the group reference in the firewall rule?  If not, how long does it usually take for a firewall rule to update it's group name if the group name changes?