Since version 2.0 we have the possibility to define a 'technical' and a 'visible' hostname for a host.
I suggest we use the same scheme for naming host groups.

This way we can use the 'technical' host group name for integration with various systems using the technical name (i.e. CUST-GR1) while retaining user readability by setting the visible name (i.e. Customer - Group 1').

Behavior should be the same as with hostnames.