ZAB CTLR EXPERIENCED OPERROR AT FL375 WHEN ISSUING CLB CLRNC TO WRONG ACFT WITH SIMILAR CALL SIGN AND IN CONFLICT WITH ANOTHER ACFT.

Narrative

I WAS WORKING SECTOR 78 BY MYSELF. I WAS OFFLINE COORDINATING WHEN ACFT X ASKED FOR FL380. WHEN I GOT BACK; I ASKED WHO HAD CALLED. ACFT X AGAIN ASKED FOR FL380. WHILE WORKING AT ACFT Z; I CLBED ACFT Z TO FL380 AND AMENDED ACFT Z'S FLT PLAN TO FL380. THINKING ALL ALONG IT WAS ACFT Z I WAS CLBING; Z HAD A JET S OF HIM; ALSO AT FL310 ALSO AT MACH .79. THE SPDS OF ACFT Z AND THE JET HAD BEEN FLUCTUATING AT TIMES SHOWING THE JET OVERTAKING THE ACFT Z. I HAD BEEN WATCHING THIS POSSIBLE CONFLICT WHEN ACFT X ASKED FOR FL380. I THOUGHT PROB SOLVED. BY CLBING ACFT X; I PUT HIM IN CONFLICT WITH ACFT Y (ACFT #2). I CAUGHT MY ERROR WHEN ACFT X'S MODE C SHOWED HIM OUT OF FL366. I RECLRED ACFT X TO MAINTAIN FL370 AND TURNED ACFT Y 20 DEGS R; BUT THIS WAS TOO LATE. ACFT X ADVISED HE HAD GONE THROUGH FL370 AND WAS GOING BACK TO FL370. ABOUT THIS TIME; CONFLICT ALERT WENT OFF. ALTHOUGH I BLAME MYSELF; 'IF' THE ACR JETS DID NOT HAVE SIMILAR CALL SIGNS (FOR INSTANCE ACR XA10 VERSUS ACR XB10) I DON'T THINK I WOULD HAVE CONFUSED THE ACFT.