CALL SIGN CONFUSION RESULTED IN FLT CREW LEAVING ASSIGNED ALT.

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WE WERE OPERATING ACR X. COMPANY ACR Y WAS BEHIND US ON A SIMILAR RTE. CTLR HAD MULTIPLE FREQS AND MULTIPLE ACFT DEVIATING FOR WX. HE WAS WORKING VERY QUICKLY. I HEARD A CLB ISSUED TO US. THE CTLR SAID THE READBACK WAS STEPPED ON AND REISSUED THE CLB. I HEARD HIM SAY SOMETHING LIKE 'EVERYBODY LISTEN; THIS IS FOR CLB TO 17000 FT.' AFTER THAT; OUR COMPANY TRIED 2 OR 3 TIMES TO SAY THAT SOMEONE HAD TAKEN THEIR CLB. I THOUGHT 'NO DUDE; YOU TOOK OURS.' THE FO WISELY LEVELED OFF. THE CTLR SAID HE SAW US CLBING AND REALIZED WE TOOK THE CLRNC. THE MISTAKE WAS CAUGHT. LUCKILY; WE HAD ONLY CLBED 200 FT OR SO (LESS THAN 300 FT). BESIDES CONGESTION; THE OTHER FACTORS ARE SIMILAR CALL SIGNS; ESPECIALLY WHEN SPOKEN FAST. ALSO; CTLR WORKLOAD -- I SWEAR THE SECOND TIME HE SAID OUR FLT NUMBER. (AT LEAST THAT IS WHAT I HEARD.) SINCE WE WERE ON SIMILAR RTES; THE INSTRUCTIONS WOULD'VE BEEN APPROPRIATE FOR BOTH OF US; THIS KNOCKING DOWN ANOTHER BARRIER PREVENTING MISTAKES. IN FACT; LATER; HE CLRED THE OTHER FLT TO OUR DEST. HE COULD'VE BEEN CONFUSED AS WELL. IN THE END; IT WAS PROBABLY A BUNCH OF FACTORS THAT CONTRIBUTED. LUCKILY; THE OTHER CREW; THE FO WITH ME; AND THE CTLR WERE ALL ABLE TO STEP BACK AND FIX THE SIT BEFORE SAFETY WAS COMPROMISED. ALSO; I READ THE CLRNC BACK WITH FLT NUMBER BOTH TIMES; BUT IT WAS LIKELY AT LEAST PARTIALLY BLOCKED.