The title of Hazrat ‘Uthmaan (radhiyallahu ‘anhu) was ‘Zun-Noorain’ (the possessor of the two lights). ‘Two lights’ referred to the two blessed daughters of Rasulullah (Sallallahu ‘alaihi wasallam), Hazrat Ruqayyah (radhiyallahu ‘anha), and Hazrat Ummu Kulthoom (radhiyallahu ‘anha).
Hazrat Hasan Basri (rahimahullah) has explained that Hazrat ‘Uthmaan (radhiyallahu ‘anhu) was given this title as he was the only person who had married two daughters of a Nabi (Hazrat ‘Uthmaan (radhiyallahu ‘anhu) married Hazrat Ummu Kulthoom (radhiyallahu ‘anha) after the demise of Hazrat Ruqayyah (radhiyallahu ‘anha)). (Siyar A’laam min Nubalaa 2/566/568)
Hazrat Nazaal bin Sabrah (rahimahullah) narrates, “We asked Hazrat ‘Ali (radhiyallahu ‘anhu), ‘Tell us something regarding Hazrat ‘Uthmaan (radhiyallahu ‘anhu).’ Hazrat ‘Ali (radhiyallahu ‘anhu) responded, ‘He was a man who would be referred to by the title ‘Zun-Noorain’ in the Mala’-ul-A’laa (assembly of angels).’” (Isaabah 4/378)
Family Relationship with Rasulullah (sallallahu ‘alaihi wasallam):
The lineage of Hazrat ‘Uthmaan (radhiyallahu ‘anhu) meets the lineage of Rasulullah (sallallahu ‘alaihi wasallam) at ‘Abd Manaaf. (Usdul Ghaabah 3/215)
The maternal grandmother of Hazrat ‘Uthmaan (radhiyallahu ‘anhu) was Baydhaa’, the daughter of ‘Abdul Muttalib. Hence, the maternal grandmother of Hazrat ‘Uthmaan (radhiyallahu ‘anhu) was the paternal aunt of Rasulullah (Sallallahu ‘alaihi wasallam). (Isaabah 4/377)
Source: Whatisislam.co.za