I do think the police helicopters do a great job and an important one at that. Among the many, like policing the motorways etc., they also are very effective in locating missing people, criminals on the run, maniac drivers etc. The ground forces rely on them heavily in these situations!
As for the names ...well, I see no harm in using names to replace lengthy explanantory titles, especially when it allows communication without giving away what is being talked about to people who shouldn't be in the know.