Small Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 3.9
Training / Qualification; Confusion; Situational Awareness
ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Executed Go Around / Missed Approach
Human Factors; Procedure
I was training somebody on the Local control position.  Aircraft X was put in position for RWY 10 while Aircraft Z was landing on RWY 23.  Once Aircraft Z was through the runway intersection the trainee cleared Aircraft X for takeoff from RWY 10 with Aircraft Y on final for RWY 23.  When it became apparent for me that there was not going to be separation I by mistake told Aircraft Z to 'Go around traffic departing RWY 10' instead of Aircraft Y.  The read back was garbled; but it appeared that Aircraft Y took the go around.  My trainee also instructed Aircraft Z to go around by mistake to which Aircraft Y responded that they were going around.  I then instructed Aircraft Y to go around.  This was all complete before Aircraft Y crossed the runway threshold.  Aircraft Y then proceeded to fly toward Aircraft X taking evasive action at the last minute to miss the aircraft.  I should have had a better idea of who was the next person on final.  Based on the chips on the magnetic board we use to track aircraft; it appeared that Aircraft Z was the next person on final.  I also allowed the trainee to go to far in this circumstance.  I should not have allowed Aircraft X to depart RWY 10.  I also should have been more specific about which direction Aircraft Y should fly instead of just calling traffic after the go around was issued.
LAF Tower Controller while instructing observes something that isn't going to work.  He sends an aircraft around but uses the wrong (similar) call sign.  Correct aircraft goes around but turns into another aircraft on the pattern and takes evasive actions to avoid it.