A PA28 CFI EXPERIENCED A SIMILAR SOUNDING CALL SIGN PROB AND BEGAN THE APCH TO RDR WITHOUT PERMISSION.

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AFTER DOING SOME AIR WORK IN A BLOCK OF AIRSPACE NE OF GRAND FORKS INTL ARPT; WE CALLED APCH WITH A REQUEST FOR VECTORS TO THE VOR RWY 17R FULL STOP. I WAS THE PIC WITH AN INSTRUMENT FLT INSTRUCTOR APPLICANT IN THE R SEAT. HE WAS 'TEACHING' ME THE APCH. WE WERE STARTING TO PICK UP THE VOR NEEDLE AND APCH ADVISED US TO EXPECT A VECTOR THROUGH THE FINAL APCH COURSE. WE REPLIED; 'ROGER.' RIGHT WHEN THE NEEDLE WAS CTRED; APCH GAVE US AN APCH CLRNC. 'ACFT XYZ; TURN L HDG 200 DEGS; DSND AND MAINTAIN 2600 FT UNTIL ESTABLISHED; CLRED VOR RWY 17R APCH.' WE READ BACK THE CLRNC; '200 DEGS; 2600 FT UNTIL ESTABLISHED; CLRED FOR THE APCH; ACFT XYZ.' SO WE STARTED OUR DSCNT DOWN TO 2600 FT FROM 4000 FT AND TURNED TO MAINTAIN THE FINAL APCH COURSE. APCH THEN TOLD US TO CONTACT ARR ON 121.1. WE MADE THE SWITCH AND CALLED THEM UP. AFTER DSNDING FROM OUR INITIAL ALT OF 4000 FT; WE WERE NOW PASSING THROUGH 3700 FT WHEN ARR CAME ON AND SAID 'ACFT XYZ; YOU WERE NOT CLRED FOR THE APCH; MAINTAIN 3700 FT; TURN R 270 DEGS.' I CALLED THEM AND SAID 'ROGER 270 DEGS; 3700 FT;' AND INFORMED THEM THAT WE WERE TOLD BY APCH WE WRE CLRED. THEN IT SOUNDED LIKE THE APCH CTLR'S VOICE THAT CAME ON THE ARR FREQ AND SAID THE CLRNC WAS FOR A SIMILAR CALL SIGN FROM THE SAME FLT SCHOOL. WE WERE NOT TOLD TO CALL APCH WHEN WE LANDED. I BELIEVE THE CAUSE OF THIS MISHAP TO DEFINITELY BE SIMILAR SOUNDING CALL SIGNS. I FLY QUITE OFTEN AROUND THE AREA AND WHEN 2 CALL SIGNS SOUND THE SAME; APCH USUALLY ADVISES YOU OF THE SIT. IT IS ALSO A TRAINING ENVIRONMENT; WITH BOTH FLT STUDENTS AND APCH STUDENTS. THE ARR CTLR APPEARED TO BE A TRAINEE AT THE TIME. THIS COULD HAVE ALSO BEEN CAUGHT WHEN WE READ BACK THE APCH CLRNC. APCH DIDN'T ADVISE US THAT IT WAS FOR XYZ; NOT XYA. I ALSO DID NOT HEAR XYZ CALL UP AND VERIFY IF THE CLRNC WAS FOR HIM. I HONESTLY BELIEVE THE CLRNC WAS READ FOR US; WHEN THE APCH CTLR MEAN TO CALL ACFT XYA. IN THE FUTURE I WILL DEFINITELY BE MORE DISTINCT WITH THE PRONUNCIATION OF MY CALL SIGN SO THE APCH CTLR CAN CATCH IT BEFORE WE MAKE A DSCNT OR TURN. I AM ALSO GOING TO BRING UP; TO OUR MGMNT; THE POSSIBILITY OF CHANGING OUR CALL SIGNS TO THE SPOKEN INDIVIDUAL NUMBERS INSTEAD OF THE GROUP-WISE FORMAT OF NUMBERS LUMPED TOGETHER.