MISTAKEN CALL SIGNS COUPLED WITH RWY AND PATTERN CHANGES AT ZZZ RESULT IN AN NMAC BETWEEN TWO TRAINING CESSNAS.

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I WAS TRAINING A PRE-SOLO STUDENT IN THE TFC PATTERN AT ZZZ ARPT IN A C152. WIND CONDITIONS WERE GUSTY AND VARYING IN DIRECTION; FAVORING RWYS XXR AND XXL FOR SHORT PERIODS; THEN FAVORING RWYS YYL AND YYR. AT APPROX XA40 LCL TIME; THE TWR CTLRS DECIDED TO CHANGE THE LNDG DIRECTION FROM RWYS XXR AND XXL TO RWYS YYL AND YYR. AS WE WERE ABOUT TO TURN R BASE FOR RWY XXR; THE TWR CTLR INSTRUCTED US TO MAKE A L 180 DEG TURN TO A L DOWNWIND FOR RWY YYL. WE COMPLIED WITH THE INSTRUCTION! ONCE ESTABLISHED ON L DOWNWIND FOR RWY YYL; ANOTHER CTLR INSTRUCTED US TO MAKE A L 180 DEG TURN. THE CTLR HAD OBVIOUSLY USED THE WRONG ACFT TAIL NUMBER. I INFORMED THE CTLR THAT WE WERE NOW ON A L DOWNWIND FOR RWY YYL. SHE IMMEDIATELY APOLOGIZED FOR THE ERROR. IMMEDIATELY THEREAFTER; WE SAW ANOTHER ACFT HEADED STRAIGHT FOR OUR ACFT; OBVIOUSLY ON A R DOWNWIND FOR RWY XXR. I TOOK CTL AND TURNED R. THE OTHER ACFT VEERED R AND DOWN; PASSING BELOW AND TO OUR L. IT APPEARS THAT THE TWR CTLR HAD INTENDED FOR THE OTHER ACFT TO MAKE 180 DEG TURN WHEN SHE MISTAKENLY USED OUR TAIL NUMBER. BOTH ACFT NARROWLY MISSED HAVING A MIDAIR COLLISION. SUPPLEMENTAL INFO FROM ACN 735561: ACFT X AND ACFT Y WERE IN R CLOSED TFC; WITH 2 DEPS; AND A SENECA INBOUND FROM THE S. ACFT X WENT AROUND DUE TO WINDS AND WAS INSTRUCTED BY THE TWR DEVELOPMENTAL TRAINEE TO REMAIN IN R CLOSED TFC AND THEIR TURN WOULD BE CALLED FOR L TFC; RWY YYL. ACFT Y STARTED TO TURN BASE AND I INSTRUCTED THE TWR TRAINEE TO TURN HIM. HE WAS TOLD BY THE TRAINEE TO MAKE L CLOSED TFC FOR RWY YYL. I WAITED UNTIL ACFT X WAS ABEAM THE TWR BEFORE I ASSUMED CTL TO MAKE THE ANNOUNCEMENT FOR THE ACFT TO MAKE A 180 DEG TURN. UNFORTUNATELY; I CALLED THEM ACFT Y RATHER THAN THEIR PROPER CALL SIGN; ACFT X. I RECEIVED NO RESPONSE FROM EITHER PLANE. I MADE A SECOND CALL TO ACFT Y 'HOW DO YOU HEAR' TO WHICH THEY REPLIED 'WAS THAT FOR ACFT Y? WE JUST MADE A 180.' MY NEXT CALL WAS 'ACFT X ARE YOU ABEAM THE TWR?' THEY REPLIED; 'YES; ACFT X HDG EBOUND.' I SAID; 'ACFT Y TFC AHEAD; AND TO YOUR L; CESSNA. ACFT X TFC AHEAD AND TO YOUR L OPPOSITE DIRECTION -- DO YOU HAVE HIM IN SIGHT?' THEY REPLIED 'ACFT X; YES; WE ARE TURNING R.'