Hi. Although there are always a lot of variations between a typical kanji (漢字) and its kana (仮名), in my personal point of view, the name would possibly be,
Minazuki Naoki = 水無月 直樹、where
水 = みず =》み (mi)
無 = な (na)
月 = つき =》づき (zuki)
[i.e., sound change from clear to muddy at the beginning after certain combinations]
直 = なお (nao)
樹 = き (ki)
Take care, and good day. / 気をつけて。良い 一日を。