FLC CLBED FROM FL280 TO FL310 ON THE BASIS OF A SIMILAR CALL SIGN ACFT CLRNC FROM FL350 TO FL310. THE FO ACKNOWLEDGED THE CLRNC TO FL310; BUT THE CTLR DID NOT HEAR IT.

Narrative

WE WERE AT 28000 FT. CHKED IN WITH ZKC. ON A DIRECT FMS FLT TO ZUNI VORTAC. HEARD AN ACR X JET CHKING ON OUR FREQ AND EVEN THOUGH WE WERE AWARE OF IT; ATC DIDN'T NOTIFY US OF SIMILAR CALL SIGNS. FL280 WAS GETTING TURBULENT AND AS I WAS FLYING THIS LEG I ASKED COPLT TO REQUEST FL310. WE BOTH HEARD OUR CLRNC TO FL310; COPLT READ IT BACK OVER THE RADIO AND THEN I PUT 31000 FT IN THE ALT WINDOW AND IN THE FMS TO LET AUTOPLT CLB ACFT. CTR DIDN'T COME BACK AND SAY WE WERE WRONG OR GOT THE WRONG CLRNC SO WE CLBED TO FL310. USUALLY IF YOU DEVIATE BY 300-500 FT FROM YOUR ASSIGNED ALT ATC WILL ASK YOU WHAT YOU'RE DOING. WE WERE GOING THROUGH 30000 FT AND I WAS MONITORING THE TCASII WHEN I SAW A POSSIBLE CONFLICT WITH AN ACFT AT OUR 12 O'CLOCK AT FL300 HEADING TOWARD US. I IMMEDIATELY STARTED A L TURN TO AVOID ACFT AND HAD FO CALL ATC TO INFORM THEM OF ACFT CONFLICT AND TURN. THAT'S WHEN ATC CAME ON AND ASKED US OUR ALT AND HE SAID WE SHOULD BE AT FL280. NOT SURE OF CONFLICTING ACFT; BUT IT WAS EITHER ACR Y AIRLINE FLT OR ACR X JET. DUE TO MY QUICK TURN TO AVOID ACFT; NEVER GOT A TCASII TA OR RA. LATERAL SEPARATION WAS ABOUT 2 MI; BUT THEY SAY VERT WAS 500-1000 FT. CTLR SAID HE NEVER GAVE US CLRNC TO FL310; DIDN'T HEAR THE FO ACKNOWLEDGE CLRNC TO FL310; BUT SAYS HE GAVE ACR X JET CLRNC FROM FL350 TO FL310. TRYING TO FIGURE THIS OUT I THINK WE ASKED FOR FL310 AT THE SAME TIME THAT ACR X JET GOT FL310. THERE WAS NO STANDBY OR WE HAVE YOUR CLRNC FROM CTR. BUT WE GOT A CLRNC TO FL310 RIGHT AFTER WE REQUESTED IT. THE FO SPOKE INTO THE MIKE AND CONFIRMED CLRNC; I SAW HIM DO IT; BUT ATC SAYS CTLR DIDN'T HEAR IT AND IT'S NOT ON TAPE. SIMILAR CALL SIGNS; ASKING FOR THE SAME ALT ALL AT THE SAME TIME; THAT'S A ONE IN A MILLION; AND ATC NEVER HEARD OR CHALLENGED US UNTIL WE WERE THROUGH 30000 FT. FATE.