I have been a paramedic (duh, my name) for many years now and I also worked with the sheriff's dept on their SAR team. We had to have an FCC license to use our radios off duty and when coordinating SAR work enroute to the mission. If we used the sheriff's radios we do not need to have an FCC license because we are on duty and have one "by proxy" I guess you would say. The same was true with all our ambulance communications.
As far as names, never ever on the medical channels, it is against patient confidentiality laws. The law enforcement side is different, names are used all the time.