Slone Fallion
A new instance should not be considered to be renamed before it is ever joined.
A new Group/Group+ instance being created for the first time is unable to be named using the VRC+ exclusive naming system, as the instance is considered to be "renamed" at that point (see "Instance rename failed" in the screenshot.
This means that my group members are unable to create new named instances (despite subscribing to present a named lobby) without being able to also close
any
group instance.
This is the only relevant permission, which affects all instance types for that group:
Manage Group Instances
Allows role to rename or close a group instance.