POTENTIAL CONFLICT BTWN A CLBING A300-600 AND A NEAR OPPOSITE DIRECTION CRJ AT 8000 FT; 10 MI W OF MEM; TN.

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TSTMS AND CUMULONIMBUS ALL QUADRANTS. BROKEN CLOUDS. VISIBILITY ABOUT 5 MI. WE WERE LEVEL AT 7000 FT MSL ON A 270 DEG ASSIGNED HDG. ATC WAS VERY BUSY ON THE RADIOS. WE HAD DEPARTED RWY 18R AND WERE MENTALLY KEEPING TRACK OF THE 2 OR 3 AIRPLANES THAT HAD DEPARTED PRIOR TO US. UNEXPECTEDLY; THE CAPT (FO WAS FLYING) NOTED TFC CO-ALT ON TCASII; AT OUR 10 O'CLOCK POS. WITHOUT A VISUAL; THE CAPT ASKED DEP CTL ABOUT IT. AS SOON AS HE UNKEYED HIS MIKE; ATC GAVE US (SO WE THOUGHT) CLB CLRNC TO 16000 FT. I STARTED A VERY GENTLE CLB; LOOKING OUTSIDE A LOT AS TCASII SHOWED AT LEAST 2 ACFT CLOSE TO US. ALMOST IMMEDIATELY; THERE WERE MORE RADIO CALLS ALONG WITH A 'TFC TFC' ADVISORY FROM TCASII; FOLLOWED BY 'MONITOR VERT SPD.' AT THIS TIME; THE CAPT OBTAINED A VISUAL AND BUMPED THE CTL COLUMN FORWARD. TCASII SHOWED CLR BELOW US; AND I PUSHED OVER; ABOUT 1/2 'G'S;' AND ALSO GOT VISUAL CONTACT. ATC TOLD THE OTHER ACFT TO CLB TO 16000 FT AND US TO MAINTAIN 7000 FT. WE HAD TOPPED OUT AT ABOUT 7200 FT; I ESTIMATE ABOUT 800 FT BELOW THE RJ; WHICH WAS HDG ABOUT 020 DEGS. APPARENTLY; THE RJ HAD DEPARTED RWY 18L AND HAD BEEN VECTORED TO THE SW BEFORE BEING ALLOWED TO TURN BACK TO THE NE AND CLB. HIS POS AND CLOSURE RATE SURPRISED US. OBVIOUSLY; THERE HAD BEEN A COM BREAKDOWN FOR A SHORT PERIOD OF TIME. IT WAS QUICKLY RESOLVED; BUT STILL CREATED A PROB. TCASII; THOUGH INITIAL INDICATIONS WERE NOT CLR; WAS VERY HELPFUL IN THE RESOLUTION. ATC MAY HAVE MISUSED OUR CALL SIGN; OR WE HEARD WRONG AND/OR STEPPED ON ATC. LESS TALKING; SLOWER TALKING; AND BETTER LISTENING WOULD HAVE HELPED; BUT I THINK ATC AND WX OVERLOADED THE CTLR. SUPPLEMENTAL INFO FROM ACN 620370: DEP ANSWERED THE RJ THAT CLRNC WAS FOR HIM TO 16000 FT; ACR X (US) MAINTAIN 7000 FT. BOTH FO AND I REALLY THOUGHT WE HEARD OUR CALL SIGN GIVEN THE CLB CLRNC. DEP NEVER MENTIONED A PROB WITH THIS EVENT. DESPITE THE 'APPARENT' MISHEARING OF A CALL SIGN; GOOD CRM AND SITUATIONAL AWARENESS ENSURED WE DIDN'T HAVE A MIDAIR. MY FO BEGAN A SLOW MANEUVER INSTEAD OF AN ABRUPT ONE THAT PROBABLY WOULD HAVE GOTTEN US RIGHT UP THERE WITH THE OTHER TFC. USUALLY AT OUR DEP ARPT; THE WBOUNDS USE THE W RWY; E AND NNE THE E RWY WITH TURNOUTS TO THE E. HVY RAIN AND LIGHTNING TO THE E HOWEVER FORCED DEP TO HAVE ALL ACFT TURN W AFTER TKOF. THIS MIGHT HAVE OVERLOADED THE CTLR.