The "Kennaiki" describes him as 'Monk-prince Naohito,' and this suggests that he was the only one among the heads of the Tokiwanomiya family who was not given the title of Imperial Prince.
ちなみにこの『建内記』では「入道直明王」とあり、常盤井宮家当主の中で唯一親王宣下を受けられなかったらしい。