AN FK100 FLC OVERSHOOTS THEIR ASSIGNED ALT WHEN ANSWERING TO THE WRONG CALL SIGN 6 MI S OF STEED INTXN WITH N90; NY.

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WHILE IN THE DSCNT PHASE OF THE FLT INTO LGA WE WERE GIVEN; AND THE FO CONFIRMED WITH HIS READBACK; A CLRNC TO 2000 FT FROM OUR ASSIGNED 3000 FT. I ALSO CONFIRMED THE ALT ON THE MCP AND INITIATED THE DSCNT. AT APPROX 2500 FT; THE CTLR REPEATEDLY CALLED; TELLING US TO IMMEDIATELY CLB BACK TO 3000 FT. WE DID NOT RECEIVE ANY TCASII WARNINGS. AFTER LNDG IN LGA; I CALLED NEW YORK APCH AND TALKED TO A SUPVR ABOUT WHAT HAD TAKEN PLACE. HE TOLD ME IT LOOKED AS IF WE HAD TAKEN ANOTHER CARRIER'S CLRNC. THE OTHER CARRIER'S CALL SIGN WAS ABXX WHILE OURS WAS ABYX. HE ALSO TOLD ME THAT THERE HAD NOT BEEN ANY CONFLICT. THE FO AND I BOTH ARE SURE WE HEARD OUR CALL SIGN WHICH ALSO MADE SENSE; CONSIDERING OUR POS APCHING THE LOC. THE SUPVR STATED THAT ON THIS APCH WE ALWAYS CROSS THE LOC FOR A L TURN TO BASE. I BELIEVE THESE TYPES OF MISTAKES WILL CONTINUE UNTIL A SYS CONSISTING OF A DATA LINK BTWN THE CTLRS AND PLTS IS BROUGHT INTO SVC. SUPPLEMENTAL INFO FROM ACN 486679: WHILE IN DSCNT PHASE OF FLT INBOUND LGA FOR ILS RWY 13; APCH GAVE DSCNT TO 2000 FT. I USED ENTIRE CALL SIGN IN READBACK KNOWING OF POSSIBLE CONFLICT/CONFUSION.