No, Gregor(y) is Gergely, common diminutive Gergő. (The repeating consonant is different in Gergely and György: International Phonetic Alphabet [g], the voiced velar plosive, versus [ɟ], the voiced palatal plosive. Wikipedia will even say them for you:
http://en.wikipedia.org/wiki/IPA_pulmonic_consonant_chart_wi...)
The surname dictionary says Györög is a variant of Györök, which is in turn a variant of Györk, a diminutive of György (=George).