ALTDEV DUE TO COM PROB BTWN ATC AND WDB FLC.

Narrative

WE WERE CLBING FROM 28000 FT TO 33000 FT WHEN I HEARD A BROKEN XMISSION WITH OUR COMPANY NAME AND FLT NUMBER. THE OTHER 2 CREW MEMBERS MISSED THE RADIO CALL ALTOGETHER. I TOLD THE FO TO ANSWER THE CALL AND HE DID WITH A 'ZJX; COMPANY NAME AND FLT NUMBER.' ZJX CAME BACK AND SAID; 'COMPANY NAME AND FLT NUMBER.' WE THEN QUESTIONED EACH OTHER AND WONDERED WHAT DID CTR WANT? I TOLD THE FO TO CALL CTR AND ASK THEM WHAT THEY HAD SAID IN THEIR LAST XMISSION. DUE TO THE HVY RADIO TFC WE WERE UNABLE TO CONTACT CTR FOR A FEW MOMENTS. WE FINALLY CONTACTED CTR WHILE CLBING THROUGH 32000 FT. THEY SAID THEY WANTED US TO STOP THE CLB AT 29000 FT. THEY THEN CLRED US TO TURN L ABOUT 40 DEGS AND CLB TO 33000 FT. CTR DID NOT SEEM TO BE ALL THAT CONCERNED. WE SAW NO TFC VISUALLY NOR WAS ANY TCASII TFC OBSERVED. IT APPEARED THAT THE CTR ACCEPTED A COMPANY NAME AND FLT NUMBER AS AN ALT CHANGE ACKNOWLEDGEMENT. A POSSIBLE FACTOR IS THE FACT THAT WE HAD AN INTERMEDIATE LEVELOFF AT 28000 FT AND I LET THE AIRSPD BUILD UP. WHEN WE WERE THEN CLRED TO CLB; BECAUSE OF OUR ADDED SPD; WE HAD AN UNUSUALLY HIGH RATE OF CLB TO 33000 FT. THIS UNUSUAL CLB RATE PROBABLY CONTRIBUTED TO THE FACT THAT THERE WAS NO CONFLICT AND CTR DID NOT SEEM TO BE CONCERNED.