B737 FLC ACKNOWLEDGES AND INITIATES CTL INSTRUCTIONS FOR ANOTHER ACFT WHILE DEVIATING AROUND WX. FLC ALLEGES ATC NEVER ADVISED TO EXPECT SIMILAR SOUNDING CALL SIGNS.

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WHILE IN CRUISE AT FL350 WE RECEIVED A CLRNC FOR WHAT WE HEARD TO BE FOR OUR ACFT TO TURN L 10 DEGS AND DSND TO FL310. THERE WERE MANY TSTMS IN THE AREA AND OTHER ACFT WERE DEVIATING FOR THEM; SO IT DID NOT SEEM UNUSUAL FOR ATC TO MAKE THIS REQUEST. MY FO ACKNOWLEDGED THE ATC REQUEST AND I TURNED THE ACFT 10 DEGS AND BEGAN A DSCNT TO FL310. AT APPROX FL343; ZAB ASKED OUR ALT. WE REPLIED THAT WE WERE PASSING FL340 FOR FL310 AS PREVIOUSLY REQUESTED. THE CTLR THEN ORDERED 20 DEG R TURN AND A DSCNT TO FL310. I DID NOT SEE ANY OTHER ACFT ON TCASII UNTIL ONE APPEARED 1100 FT BELOW AND APPROX 10 MI BEHIND US. NO PROBS WERE PERCEIVED UNTIL SEVERAL MINS LATER; AFTER WE HAD BEEN DEVIATING EXTENSIVELY FOR WX -- WITH ATC APPROVAL -- THAT WE WERE ADVISED TO CALL ZAB ON LNDG FOR A POSSIBLE PLTDEV. WE REMEMBERED HEARING ANOTHER ACFT WITH A SIMILAR CALL SIGN; WHICH WE LATER FOUND OUT TO BE ACFT #2. IF THE TURN AND DSCNT CLRNC WERE FOR ACFT #2 AND NOT ACFT #1; HE MAY HAVE STEPPED ON OUR READBACK; OR WE MAY HAVE STEPPED ON HIS. AT NO TIME WERE WE EVER ADVISED THAT THERE WAS ANOTHER ACFT ON FREQ WITH A SIMILAR SOUNDING CALL SIGN. THE SIMILAR CALL SIGNS; EXTENSIVE DEV FOR WX; AND CONGESTED RADIO COMS WERE ALL CONTRIBUTING FACTORS TO THIS POSSIBLE DEV. SUPPLEMENTAL INFO FROM ACN 409090: THE OCCURRENCE HAPPENED WHILE WE WERE CLRED DIRECT TO ZUNI VOR AT FL350. WHILE WE WERE ON THIS FREQ; WE HEARD ACFT #2. WE WERE NEVER TOLD ABOUT A CONFLICTING CALL SIGN.