You can have unique radio call signs or group names for your units / groups.

group this setGroupId ["Some name for the group"];

It is actually very simple, there is no specific name and ID number, you can make it yourself like below.

group1 this setGroupId ["Blackjack Six"];
group2 this setGroupId ["Delta 1"];

Headquarters call sign doesn't work, commented is what it returns as call sign:

PMCHQ = [ West, "HQ" ]; PMCHQ SideChat "HQ"; // crossroads
PMCHQ = [ West, "BASE" ]; PMCHQ SideChat "BASE"; // base
PMCHQ = [ West, "AIRBASE" ]; PMCHQ SideChat "AIRBASE"; // base
PMCHQ = [ West, "Papa_bear" ]; PMCHQ SideChat "papa_bear"; // base

Would have been nice to have virtual entity as custom HQ call sign, but now you must add single unit for that side you want to create it.