C182 ON IFR TRAINING FLT EXPERIENCED CONFUSION WITH N90 CTLR.

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I WAS PIC FLYING AN INST REQUALIFICATION FLT WITH ANOTHER PLT FLYING AS SAFETY PLT. TKOF FROM BRIDGEPORT (SIKORSKY) ENRTE TO OXFORD; CT; FOR PRACTICE APCHS. CONTACTED NY APCH AND WAS GIVEN XPONDER CODE AND IDENTED BY NY APCH. I WAS INFORMED THAT THERE WOULD BE A DELAY OF 30 MINS TO EFFECT PRACTICE APCHS TO OXC. I THEN TOLD NY APCH THAT I WOULD GO TO DANBURY FOR MY PRACTICE APCHS. THE CTLR GAVE ME A HEADING AND TOLD ME TO CONTACT ANOTHER NY CTLR; WHICH I DID. MADE CONTACT WITH NY APCH ON THAT FREQ AND PROCEEDED TO MAKE 2 APCHS INTO DRX; AS CLRED BY APCH CTL AND DXR TWR. AFTER THAT I FLEW BACK TO OXC. PROCEEDED WITH APCH CLRNC TO OXC; AND MADE CONTACT WITH PREVIOUS CTLR. HE INFORMED ME THAT HE HAD LOST CONTACT WITH ME EARLIER; AND HAD ASSUMED THAT I HAD A MISHAP SINCE WE WERE NOT IN CONTACT. ALL THIS WAS IN ERROR ON THE CTLR'S PART AS HE MISIDENTED MY FLT WITH ANOTHER! WHEN I EXPLAINED TO HIM WHAT TRANSPIRED; HE REALIZED HIS ERROR AND WAS VERY APOLOGETIC TO ME FOR THE MISTAKE HE HAD MADE. HE ACKNOWLEDGED THAT HE RECALLED THE SIT OF MY DIVERTING TO DXR AND HANDING ME OFF TO THE NY APCH CTLR FOR THAT SECTOR.