Maybe it says a lot about how you see your own operation. I used to use 'Air Ambulance' as the public get what you mean far easier and also because I see the AA as an adjunct to the ground service. A tool that is part of the dispatchers toolkit when it comes to dealing with anything that might prejudice the ongoing efficiency of the service to the whole community.
HEMS is industry 'shorthand' but if you are not careful it can be used to paint yourself out of the big picture when it comes to overall effectiveness of the Ambulance service.
G.