this name didn't make it to Poland, so we don't have a Name Day for you, sorry :(
BUT there's hope, our Name Days are based on Catholic/Christian calenders, so if there's a saint patron in other Catholic calender/country, you can use it.
(according to Italian Wikipedia) it exists in Italian (as Noemi, with the variant Naomi) coming from Hebraic Noam (= "pleasure")
and the most important:
there's a Name Day (even 2 possibilities)
4 June (together with Saint Ruth, Naomi's daughter-in-law)
According to other sources: 14 December