You're on the right track with reincarnation:
Renatus is
Re = again + natus = born. Feminine is
Renata. (Reincarnation is re = again, in = in, and carn- = flesh.) As for your day component, diem is a form of dies (accusative or objective case, used for direct object and after some prepositions!) but dia really isn't. And, I must say, I'm not convinced by the vowel change, A to E. What language is Renediem supposed to be? The H at the end of Renediah makes it look Semitic; have they both got the same origin?