I started working ambulances front and back in the sixties and retired in the nineties. During that period of time the information we were 'supposed' to know had more to do with medical/mental state rather than personal information. I can't remember ever giving a name over the radio. Physical descriptions, general descriptions sure, but not names. It just wasn't 'done', you know? I don't think I was ever told to -not- give names, it was just assumed I guess. No identifying numbers either, that was all on paper. A time or two I let the hospital know in a 'round-about' way who the patient was but never by name or 'nickname'.
There were a couple of 'medical-terms' used also, such as the patient having a 'subdural-fecal-toma', or was suffering from 'ceramic-syndrome'. That's different though. I won't say what they mean, but you can figure it out... PD had there own set of describers.