ENRTE A300 CONFUSED CALL SIGN AND STARTED CLB WITHOUT ATC CLRNC.

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OUR FLT NUMBER FOR THIS LEG WAS ABC. WE DEPARTED MEM DIRECTLY BEHIND ANOTHER EBOUND COMPANY HVY ACFT WHOSE FLT NUMBER WAS ADC. WE WERE VERY AWARE OF THE SIMILARITIES; AND EACH CTL FACILITY ADVISED US THAT COMPANY FLT ADC WAS ALSO ON THE FREQ. WHEN WE XFERRED TO THE MEMPHIS LOW SECTOR WE WERE CLRED TO FL230. PRIOR TO HANDING US OFF TO THE HIGH SECTOR; WE WERE ADVISED THAT THEY WERE VERY SATURATED AND THAT WE MIGHT BE HELD AT FL230 FOR A SHORT WHILE. WE HEARD A FREQ CHANGE FOR WHAT SOUNDED LIKE OUR FLT NUMBER; HOWEVER; THERE WAS ENOUGH AMBIGUITY IN THE SYNTAX THAT WE QUESTIONED WHICH ACFT THE CHANGE WAS FOR; AND WERE ADVISED THAT THE CHANGE WAS FOR ADC. A FEW MINS LATER; WE WERE HANDED OFF TO ZME HIGH SECTOR. WHEN WE CHKED IN; WE WERE CLRED TO MAINTAIN FL230; AND WERE AGAIN ADVISED THAT COMPANY FLT ADC WAS ALSO ON THIS FREQ. ABOUT 4 MINS LATER WE ACKNOWLEDGED A CLRNC TO CLB AND MAINTAIN FL330. IT IS IMPORTANT TO NOTE THAT AS WE WERE ANTICIPATING BEING AT FL230 FOR AN EXTENDED LENGTH OF TIME; THERE WERE NO PRECONCEIVED EXPECTATIONS TO RECEIVE THIS CLRNC. AS WELL; AS PF; I SET THE NEW ALT IN THE FCP WINDOW AT THE SAME TIME AS THE FO ACKNOWLEDGED RECEIVING THE CLRNC. THE POINT IS THAT THERE WERE NO DISTRS; WE WERE VIGILANT THAT A SIMILAR CALL SIGN WAS ON THE FREQ; AND THERE WAS NO AMBIGUITY AS HAPPENED IN THE CITED FREQ CHANGE. THE FO AND I BOTH INDEPENDENTLY HEARD WHAT SOUNDED LIKE A CLRNC FOR ABC TO CLB AND MAINTAIN FL330. AFTER ACKNOWLEDGING THE CLRNC WE BEGAN THE CLB TO FL330. THERE WAS NO CHALLENGE TO OUR ACKNOWLEDGEMENT BY EITHER ZME OR ANY OTHER ACFT. AS WE PASSED THROUGH APPROX FL265 WE WERE QUERIED ABOUT OUR CLB BY ZME. WE INFORMED THEM THAT WE WERE CLBING TO FL330 PER OUR CLRNC. WE WERE ADVISED THAT THE CLB CLRNC WAS INTENDED FOR FLT ADC. AFTER A BRIEF MOMENT OF SILENCE; WE ASKED CTR WHERE THEY WOULD LIKE US. WE WERE SUBSEQUENTLY CLRED TO MAINTAIN FL270. AT THIS POINT IT IS UNCLR WHETHER ZME OR WE COMMITTED THE ERROR. IN ANY EVENT; OUR COMPANY IS WELL AWARE THAT THEY OFTEN PLACE FLTS WITH VIRTUALLY INDISTINGUISHABLE FLT NUMBERS IN CLOSE PROX. THEY ACKNOWLEDGE THAT THIS IS A SAFETY ISSUE; YET THEY HAVE DONE VERY LITTLE TO RESOLVE THIS CONCERN.