ATC INTERVENED AND SEPARATED 2 MLG ACR ACFT AT HIGH ALT DUE TO ATC CONFUSION OF SIMILAR SOUNDING ACFT NUMBERS.

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OUR CALL SIGN WAS ACR X. AN ACR Y WAS ALSO ON FREQ. WE WERE PROCEEDING N TO DJB VOR AT FL240 HDG APPROX 360 DEGS. HE DID NOT SAY IF THIS WAS AN ALT; A HDG; OR A SPD; BUT LOGICALLY IT WAS A SPD ASSIGNMENT SINCE WE WOULD BEGIN OUR DSCNT SOON; AND A 310 DEG HDG WOULD TAKE US OFF COURSE. SO I READ BACK 'ROGER; ACR X; 310 KTS.' A FEW SECONDS LATER; WITH SOME APPARENT URGENCY; HE GAVE US A L TURN TO 270 DEGS (A 90 DEG TURN OFF COURSE). HE ALSO GAVE A TURN TO ACR Y AND THEN ASKED HIM TO TIGHTEN HIS TURN. THE PLT OF ACR Y SAID THEY COULD TURN NO TIGHTER. THE CTLR GAVE FURTHER INSTRUCTIONS TO ACR Y AND THE CREW OF ACR Y; APPARENTLY REFERRING TO HIS TCASII DISPLAY; SAID 'I DON'T THINK YOU WANT US TO DO THAT; YOU'LL TURN US RIGHT INTO HIM.' THE CTLR CHANGED HIS MIND AND AGREED. HE THEN CLRED MY FLT DIRECT TO DJB VOR. THE CAPT OF ACR Y ASKED ME TO COME UP ON COMPANY FREQ. HE STATED THAT HE THOUGHT THE CTLR ALMOST RAN HIS FLT INTO OURS. WE NEVER GOT ANYTHING ON OUR TCASII BUT HE HAD SOMEONE ON HIS. WE BOTH AGREED THAT THE CTLR PROBABLY GOT OUR CALL SIGNS CONFUSED. NEITHER OF US BELIEVED THAT WE HAD MADE AN ERROR. CONTRIBUTING TO THIS IS OUR AIRLINE'S REFUSAL TO ELIMINATE SIMILAR SOUNDING CALL SIGNS FROM ITS SYS. WE COUNTED 5 FLT NUMBERS ALL ENDING IN '3' ON FREQ AT THE SAME TIME.