REPORTER CTLR GAVE DESCENT CLRNC TO THE WRONG ACFT RESULTING IN LESS THAN STANDARD SEPARATION IN OCEANIC AIRSPACE.

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DUE TO WX; ACFT CALLING ON BOTH FREQS CUTTING ONE ANOTHER OUT; HAD TO PUT 1 FREQ ON SPEAKER. SIMILAR SOUNDING CALL SIGNS--LGT X (BBDG) AND LGT Z (BDCG). FAILED HDOF WITH MIA. HAD TO MANUALLY COORDINATE. NOT LISTENING TO ACFT CALL SIGH WHEN ACFT READ BACK CLRNC. THE PROB WAS DISCOVERED WHEN I SCANNED THE SCOPE AND OBSERVED LGT Z (BDCG) LEAVING FL350; TOOK IMMEDIATE ACTION. THE SITUATION OCCURRED BECAUSE OF HUMAN ERROR--MINE. I MISSED A READBACK OF A CLRNC BECAUSE I WAS PREOCCUPIED WITH AN ACFT 300 MI AWAY. I HEARD THE READBACK OF THE CLRNC BUT I MISSED THE CALL SIGN. ALSO I WAS WORKING 2 FREQS. IF EVERYONE WOULD HAVE BEEN ON ONE FREQ THIS MAY HAVE BEEN ADVERTED. HISTORY--134.3 HAS A BLIND SPOT; ABOUT 170-240 MI NW OF SJU IN THE VICINITY OF ELMUC. A VCR WAS FILED ON THAT. THE RESPONSE WAS TO PUT A FREQ (135.7) AT BQN. LGT X (BBDG) REQUESTED LOWER. CLRED LGT X (BBDG) TO CROSS 40 MI NW OF SJU AT 10000'. PUT LGT Z (BDCG) ON A 170 DEG HDG. WENT BACK TO LTT V TO WORK ON GETTING HIM ON G449. D-SIDE CALLED TTPP TO ADVISE ACFT WAS W OF COURSE FOR WX. OBSERVED LGT Z (BDCG) LEAVING FL350. ASKED HIM HIS ALT; THEN TURNED HIM TO A HDG OF 100 DEGS. I THEN DSNDED WDB R TO FL290; TO DSND NOW THROUGH FL310. CALLED TFC. TOOK CARE OF REMAINING TFC. TURNED MYSELF IN. AFTER LISTENING TO THE TAPES I DISCOVERED THAT LGT Z (BDCG) REQUESTED LOWER AND THAT I DSNDED LGT Z (BDCG) AND PLT READ BACK THE CLRNC.