Skyhawk 172/Cutlass 172
Flight Crew Instrument; Flight Crew Commercial; Flight Crew Flight Instructor
Flight Crew Last 90 Days 250; Flight Crew Total 700; Flight Crew Type 700
Situational Awareness
ATC Issue All Types; Conflict NMAC
General None Reported / Taken
Human Factors; Procedure
Requested clearance for NW departure. Controller cleared us [for] takeoff. After receiving clearance; prior to departure; I asked if they wanted us to make left or right traffic. It is usually left traffic; but I wanted to be sure because they didn't say anything. They gave us a left downwind departure. So I made left traffic and once clear of the pattern (approach end); I turned NW. The controllers don't usually give us a frequency change; they just let us go to the practice area; and don't want to hear from us to request one. I usually monitor tower until way beyond the airspace so that I can hear who is coming in. I was almost clear of D airspace. I was explaining holding procedures to my student when I hear tower make a call for another airplane that belonged to the school I work for. I knew that plane was not up at that time so I was listening again in case they misidentified my call sign (completely different from the other plane they called) as often happens at this airport. They had in fact misidentified my callsign; and had not realized it. They were calling to point out traffic. I looked at my TCAS and it showed several airplanes in my area; so I started looking for the traffic. The TCAS is often unreliable; so I try to avoid using it as my primary traffic avoidance; particularly in busy airspace. This time it identified the traffic as 400 FT above me. I did not see it until it passed right over us; as it was a hazy day. Tower then yelled at me for flying along the final approach course for one of the other runways. I was merely following the departure procedure set by our school; while also trying to fly the clearance given to me. The incoming plane was very close and there was no time to avoid. Fortunately; there were a few hundred feet of separation. Had the controller correctly identified my callsign; I could have picked out the traffic sooner. They were also speaking to that incoming plane; and could have given them a vector to avoid us when we didn't respond--because they used the incorrect callsign for us.
Cessna 172 instructor pilot reported an NMAC departing OPF airport.