B737 CREW RESPONDED TO A CLRNC GIVEN TO ANOTHER ACFT WITH SIMILAR CALL SIGN.

Narrative

AFTER TKOF FROM DEN; DEP CTL ISSUED MY FLT (ACFT X) A HDG TO JOIN THE PLAINS2. HCT TRANSITION AND A CLB TO FL230. THIS CLRNC WAS ISSUED DURING A TIME OF HIGH COCKPIT WORKLOAD. UNFORTUNATELY; THE CLRNC WAS FOR ACFT Y. THE CTLR NEVER CORRECTED MY READBACK OF THE CLRNC. I READ THE CLRNC BACK USING MY CALL SIGN. IT BECAME CLR TO ME THAT I ACCEPTED ACFT Y'S CLRNC WHEN ACFT Y CLAIMED THAT ACFT X TOOK HIS CLRNC. CTLR WORKLOAD WAS HIGH AND IT TOOK A WHILE FOR THE CTLR TO RESPOND TO ACFT Y. WHEN THE FREQ WAS CLR I ASKED THE CTLR IF I HAD TAKEN ACFT Y'S CLRNC AND HE SAID YES. I THEN MENTIONED TO THE CTLR THAT I WAS NOT AWARE OF ANOTHER AIRLINE WITH THE EXACT SAME FLT NUMBER AS MINE BEING ON THE FREQ. HE RESPONDED TO ME THAT HE WAS TOO BUSY TO TELL ME. I DID IN FACT TAKE THE WRONG CLRNC; BUT I MUST POINT OUT THAT THE CTLR WORKLOAD IS TOO HIGH WHEN HE DOES NOT HAVE TIME TO RELAY SUCH IMPORTANT INFO SUCH AS ANOTHER ACFT WITH THE EXACT SAME FLT NUMBER IS ON THE FREQ. THE CTLR WAS BUSY AND I WAS BUSY. THIS MISTAKE WAS EASY TO DO UNDER THESE CIRCUMSTANCES. IT'S NICE TO TRY AND MOVE AIRPLANES; BUT NOT AT THE EXPENSE OF BASIC SAFETY PRECAUTIONS. IN THIS CASE THERE WAS NO CONFLICT BUT THERE COULD HAVE BEEN.