MIL Y CLB THROUGH OCCUPIED ALT HAD LTSS FROM MIL Z. SYS ERROR.

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I WAS WORKING SECTOR R6 AT ZAN; WAS NOT BUSY; ONLY ABOUT 7 ACFT ON FREQ. JUST TOOK A HDOF FROM ANC APCH ON MIL X AND EXPECTED HIM TO CALL SOON. HE WAS THE ONLY ACFT I HAD ON RADAR AROUND ANC APCH. MIL Y CALLED ME AT FL200. IN MY MIND I WAS THINKING MIL X; BUT IN REALITY I CLBED MIL Y TO FL350. MIL Y SHOULD HAVE BEEN TALKING TO AN ADJOINING SECTOR. REALITY SET IN WHEN THE REAL MIL X CHKED IN CLBING TO FL220 AND THE SECTOR NEXT TO ME SAID HE HAD A MIL Z AT FL210 TAKING EVASIVE ACTION. MIL Z WAS AN OVERFLT FROM MY SECTOR TO THE S AT FL210. ANC APCH AIRSPACE IS DSNDING TO FL200. ALTHOUGH NOT REQUIRED; A POINTOUT WOULD HAVE BEEN HELPFUL TO ANC APCH SO THEY WOULD NOT HAVE PUT MIL Y UNDER MIL Z. ANOTHER FACTOR I FEEL SHOULD BE CONSIDERED IS THE SIMILAR SOUNDING CALL SIGNS MIL X AND MIL Y. WHY DID MIL Y COME UP ON MY FREQ; DID HE TAKE MIL X COM CHANGE FROM ANC APCH? THE HUMAN FACTOR OF NOT HEARING THE DISTINCTION BTWN MIL Y AND MIL X SHOULD BE ATTRIBUTED TO MY INATTENTIVENESS. THE END OF THE SHIFT ON A ROTATING SCHEDULE WHICH IS VERY HARD ON MY BIOLOGICAL TIME CLOCK.