SINGLE ENG IFR STUDENT TRAINING ON MULTI ENG WITH IFR FLT PLAN LANDS AT WRONG ARPT. BOTH STUDENT AND INSTRUCTOR REALIZE MISTAKE AND DEPART REQUESTING VECTORS TO CORRECT ARPT.

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BEING INST RATED IN SINGLE ENG; I FILED A MULTI ENG IFR FLT PLAN AND PUT MY NAME IN INSTEAD OF MY INSTRUCTOR BY ACCIDENT. WE SHOT A VOR/DME RNAV OR GPS RWY 12 APCH INTO FARIBAULT. AS WE BROKE OUT INTO VFR WE CANCELED OUR IFR FLT PLAN. ARPT WAS IN SIGHT WITH RWY IDENTIFIERS RWY 12/30 TO FIND OUT IT WAS WRONG ARPT. WE HAD LEFT OUR SQUAWK CODE IN AFTER TAKING OFF. APCH TOLD US TO CALL THEM ARRIVING AT FARIBAULT. WE WERE VFR TO FARIBAULT. SHOULD HAVE LISTENED TO MY INSTRUCTOR MORE THOROUGHLY WHILE PREPARING AND FILING FLT PLAN. WORKLOAD WAS HVY WHILE TRAINING IN THE TWIN. SUPPLEMENTAL INFO FROM ACN 387465: UPON SEEING THE ARPT I CANCELED MY IFR CLRNC AND EXECUTED A NORMAL LNDG AT THE WRONG ARPT. OWATONNA IS AN UNCTLED ARPT. AFTER REALIZING THE ERROR I TOOK OFF VFR AND CONTACTED MINNEAPOLIS APCH TO GET VECTORS TO FARIBAULT. MINNEAPOLIS APCH GAVE ME THE PHONE NUMBER TO CONTACT THEM ONCE I ARRIVED IN FARIBAULT. IN THE FUTURE I NEED TO PAY BETTER ATTN TO THE TITLE OF THE APCH PLATE AND MAINTAIN SITUATIONAL AWARENESS AT ALL TIMES.