Uthman Radiallahu anhu grandmother’s name was Umm Hakeem Al Baydaa Bint Abdul Muttalib, the paternal aunt of the Prophet sallallahu alaihi wassallam. See Tahdheebul Kamaal 19/445.
Al Aamiree said in Riyaadul Mustataabah page 156,
“He is the closest of the ten (who were given glad tidings of paradise) in lineage to the Messenger sallallahu alaihi wassallam after Ali” End translation.
There were 13 from the companions who’s name was Uthmaan. See Shaykh Abu Amr book Fiqhul Akbar V.2
Majid Jawed Al-Afghanee