LESS THAN LEGAL SEPARATION OF 2 ACFT ON CLB.

Narrative

ACFT X; AN E120; WAS A CLE DEP ENRTE TO BUF CLBING TO 17000 FT VIA THE DJB 054 DEG RADIAL.FAILS./.BUF. ACFT Y; AN RNAV EQUIPPED G3; WAS A CLE DEP ENRTE TO HPN CLBING TO 13000 FT VIA THE DJB 054 DEG RADIAL.FAILS.DNY;VALRE2.HPN. X HAD LEFT 13000 FT IN HIS CLB. IMMEDIATELY AFTER ISSUING 13000 FT TO Y; I CLRED HIM DIRECT TO DNY; WHICH HE READ BACK IN ACKNOWLEDGEMENT. APPROX 1 MIN LATER Y QUESTIONED THE DIRECT CLRNC. AGAIN; I ISSUED DIRECT DNY AND A CLB CLRNC TO FL230; BOTH OF WHICH HE ACKNOWLEDGED. APPROX 30 SECONDS LATER; HAVING STOPPED X AT 15000 FT; I REALIZED THAT I WOULD NOT HAVE SUFFICIENT VERT SEPARATION ONCE LATERAL SEPARATION WAS LOST. Y WAS TURNED R TO A 120 DEG HDG FOR TFC. MOMENTS LATER; Y WAS OBSERVED LEAVING 16000 FT; AND RECLRED DIRECT DNY. AT THIS POINT Y ASKED FOR THE SPELLING OF DNY; WHICH I MISSED. 90 SECONDS LATER; Y ASKED FOR THE 3-LETTER IDENT FOR DNY; TO WHICH I RESPONDED PHONETICALLY. 3 MINS AND 30 SECONDS ELAPSED FROM THE TIME Y INITIALLY READ BACK THE DIRECT CLRNC; AND FINALLY WAS MADE TO UNDERSTAND THE DIRECT CLRNC.