CREW MISSED A HEADING CHANGE DURING DSCNT AND HAD A CONFLICT AIRBORNE WITH ANOTHER ACFT.

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UPON INITIAL CONTACT GIVEN DSCNT FROM 10000 FT TO 5000 FT; 'EXPECT RWY 27.' SHORTLY THEREAFTER; TOLD 'EXPECT RWY 18R AND CONTACT FINAL CTLR.' 'FINAL' CTLR WAS WORKING MANY ACFT; 99% OUR COMPANY; AND AT LEAST ONE WITH A SIMILAR SOUNDING FLT NUMBER. ASSIGNED SPD 210 KTS; THEN CLRED TO 4000 FT; HEADING 270 DEGS. LEVELING 4000 FT; ASSIGNED 3000 FT; SLOW TO 180 KTS. I BEGAN A 500 FPM DSCNT AND ALLOWED IAS TO SLOWLY DECREASE. AT ABOUT 3500 FT; ATC CLRED THE FLT WITH SIMILAR CALL SIGN '200 KTS AND 2000 FT.' PF THOUGHT THE SPD; ALT ASSIGNMENT WAS FOR US AND 'ANSWERED' ATC; BLOCKING THE OTHER FLT'S ACKNOWLEDGMENT. ATC CORRECTED US; RECLRED THE OTHER FLT; THEN ASKED OUR SPD (200 KTS; DECREASING). THEN; IN A VERY EXCITED VOICE HE SAID 'TURN L HDG 180 DEGS NOW.' AS WE TURNED; WE OBSERVED AN OPPOSITE DIRECTION ACFT WE HAD BEEN WATCHING; GO OVER US APPROX 1000 FT ABOVE. REMAINDER OF FLT WAS NORMAL VECTORS FOR THE APCH. ON POSTFLT THE 3 OF US (FLC) DISCUSSED EVENT. NONE OF US BELIEVE WE MISSED A HEADING ASSIGNMENT. POSSIBILITIES ARE ATC FORGOT DUE TO WORKLOAD AND SIMILAR SOUNDING CALL SIGNS; OR HE GAVE IT TO US DURING THE BLOCKED XMISSION; OR WE MAY (NOT LIKELY) HAVE MISSED IT. WE DON'T BELIEVE THERE WAS A TFC CONFLICT THIS TIME; BUT WE HAVE NO WAY OF KNOWING (NO TCASII). IF WE ARE CORRECT IN THAT WE DID NOT MISS THE HEADING ASSIGNMENT; THEN THE MOST LIKELY FACTOR WOULD BE ATC WORKLOAD AND WITH SIMILAR CALL SIGNS ATC THOUGHT HE GAVE US A NEW HEADING; OR HE GAVE '180 KTS' INSTEAD OF '180 DEGS;' WHICH HE MIGHT HAVE MEANT. THE COMPANY 'AIRLINE SCHEDULING' DEPT CTLS FLT NUMBERING; AND WITH APPROX 130 FLTS ARRIVING IN AN APPROX 2 HR PERIOD THERE ARE BOUND TO BE SIMILAR SOUNDING CALL SIGNS; BUT PERHAPS THERE IS SOMETHING THEY CAN DO TO REDUCE THE NUMBER. SEVERAL PLTS HAVE SUGGESTED THIS THROUGH OUR INTERNAL FLT SAFETY DEPT; BUT THE COMPANY IS RELUCTANT TO CHANGE FLT NUMBERING FOR NOW DUE TO THE 'SYS' CURRENTLY IN PLACE.