ZMP CTLR; MISUNDERSTANDING WHO HE ISSUED A DSCNT CLRNC TO; RECLRS AN A319 BACK TO FL350 AND CORRECT A DSCNT CLRNC TO ANOTHER ACR WITH A SIMILAR SOUNDING CALL SIGN.

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AT XA00Z; AT FL350; JUST SWITCHED FROM ZAU TO ZMP. THE CTLR ACKNOWLEDGED OUR CHK ON FREQ AND ADVISED US THAT TURB WAS AHEAD AT FL350. THE CTLR RECOMMENDED WE DSND TO FL310. THE FO WAS HANDLING RADIO COMS; BUT EATING DINNER AT THE SAME TIME. HE ACKNOWLEDGED ZMP. AS HE WAS EATING; I RECONTACTED ZMP AND ASKED THE CTLR IF POSSIBLE TO GET US FL310 BEFORE WE REACHED THE AREA OF TURB. THE CTLR REPLIED; 'WILL FIX THAT PROB RIGHT NOW; DSND TO FL310.' I ACKNOWLEDGED 'THANK YOU; WE'RE DSNDING TO FL310.' WITHIN 30 SECONDS OF THIS XMISSION; ANOTHER ACR ADVISED CTR THAT HE ALSO WANTED TO DSND TO FL310 FOR THE TURB. THE MSP CTLR THEN STATED; 'I JUST CLRED YOU TO FL310.' A MOMENT LATER; THE MSP CTLR REALIZED HIS MISTAKE AND STATED 'ACR X; MAINTAIN FL350.' AT THIS POINT; WE WERE AT FL345 AND IMMEDIATELY RETURNED TO FL350. THE CTLR THEN STATED THAT HE WOULD SHORTLY GET US FL310 AND AGAIN CLRED ACR Y TO FL310. WE QUERIED THE CTLR AS TO WHETHER THERE WAS ANY PROB AND THE CTLR STATED THAT THERE WAS NO PROB. THIS SIT OCCURRED; AS I SEE IT; BECAUSE THE CTLR DID NOT ADVISE US THAT HERE WAS A SIMILAR CALL SIGN ON THE FREQ ON OUR FIRST CONTACT. THE CTLR MISUNDERSTOOD WHO HE WAS TALKING TO WHEN WE ASKED FOR A DSCNT TO FL310. THE CTLR ALSO DID NOT CLRLY IDENT OUR CALL SIGN TO DSND TO FL310. RATHER; HE STATED HE COULD FIX THE PROB BY CLRING US TO FL310 AT THAT TIME. I FURTHER DID NOT CLRLY IDENT THAT ACR X WAS DSNDING TO FL310; RATHER STATED 'THANK YOU; DSNDING TO FL310.' THERE WERE NO TFC CONFLICTS AND I FEEL THAT ALL PARTIES LEARNED AN IMPORTANT LESSON TO BE SURE TO IDENT THE AIRLINE AND FLT NUMBER IN EVERY XMISSION. SUPPLEMENTAL INFO FROM ACN 602952: ONE THING THAT I WOULD MENTION WAS THAT 2 DIFFERENT SOUNDING PLTS FROM THE SAME FLT MAY HAVE LENT TO ANY CONFUSION ON THE PART OF THE CTLR. I DO NOT REMEMBER SPECIFICALLY IF MY CAPT USED OUR CALL SIGN WHEN HE SPOKE TO THEM AFTER MY QUERY REGARDING TURB.