From Rasputine by Spiridovitch, pg. 73 (my translation):
"That year (1906) or the following year, Rasputin received the name "Novyk". His daughter Matrona explained that it happened one day when the Tsarevich greeted Grigori with the words "Papa, Papa! here is the new one (Novy)!" This nickname pleased Their Majesties, and so they gave him this new name. The enemies of the Staryets said that they had changed his name because Rasputin as a name came from "rasputsvo" or debauched, which served as proof to them that his family had long been famous for their vices. However, as to the Rasputin family themselves, they explain that the name came from the word "rasputye" or the crossing of roads, and moreover this is the far more likely explanation. In any event, changing Rasputin's name only served to give new ammunition to his enemies."