PLT OF AN SMT SINGLE ENG LAND TURBOPROP ATX ACFT WAS NOT HANDED OFF TO THE TWR AFTER BEING CLRED FOR AN APCH BY APCH CTL.

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A COMPANY CHK AIRMAN WAS GIVING ME A 135.297/.299 CHK. I TOLD GSO CLRNC THAT I WAS BEING GIVEN A CHKRIDE AND WOULD LIKE A TOTAL OF 3 PRACTICE APCHS; AN NDB RWY 33; AND A VOR/DME RWY 15 AT INT; A NEARBY ARPT; THEN AN ILS 23 BACK INTO GSO. I REQUESTED FLYING THE APCHS IN VMC. GSO CLRNC GAVE US THE CLRNC AND WE TAXIED OUT AND DEPARTED. GSO APCH GAVE US VECTORS TO THE FINAL APCH COURSE NDB RWY 33 AT INT; A TWR CTLED FIELD; AND CLRED US FOR THE NDB RWY 33 APCH. AFTER PASSING THE FINAL APCH FIX AND DSNDING TO THE MDA; WE REALIZED THAT GSO APCH HAD NOT GIVEN US A FREQ CHANGE TO INT TWR. I THEN SWITCHED TO INT TWR WITHOUT NOTIFYING GSO APCH; SINCE WE WERE CLOSE TO THE FIELD. WHEN I SWITCHED FREQS; INT TWR HAD NO INFO ON US; AND ASKED OUR POS. I TOLD INT TWR WE WERE CLRED FOR THE NDB RWY 33 APCH; AND WERE ALMOST OVER THE FIELD. A FEW SECONDS WENT BY; BUT INT TWR STILL COULD NOT FIGURE WHAT WE WERE DOING THERE. BY THAT TIME; THE TIME FOR THE APCH HAD EXPIRED; AND I PROCEEDED WITH THE PUBLISHED MISSED APCH PROC AND CONTACTED GSO APCH. I ASKED GSO APCH IF I SHOULD NOT HAVE CONTACTED THE TWR. ALL I HEARD WAS A SINGLE SYLLABLE; UNINTELLIGIBLE RESPONSE; THEN GSO APCH ASKED OUR INTENTIONS. WE SAID WE WANTED A TURN IN THE HOLDING PATTERN DEPICTED ON THE MISSED APCH PROC FOR NDB RWY 33; THEN VECTORS FOR A 20 NM DME ARC TO THE VOR/DME RWY 15 APCH. GSO APCH THEN CLRED US AS WE REQUESTED; CLRED US FOR THE VOR/DME RWY 15 WHEN WE RPTED TURNING INBOUND ON THE FINAL; AND SWITCHED US TO INTO TWR. INT TWR WAS EXPECTING US WHEN WE SWITCHED THIS TIME; BUT SAID NOTHING ABOUT OUR NDB RWY 33 APCH OR LEAVING THEIR FREQ AND RETURNING TO GSO APCH.