Grading: Its chain is hasan because of Ibn Abi al-Zinad (whose name is Abd al-Rahman); he is "saduq, hasan al-hadith" (truthful, good in hadith).
Technical note / Defect ('illah): The author (al-Hakim) confined himself to this chain only to establish Uthman bin Affan's kunyah "Abu Abd Allah", and did not mention the full hadith. That hadith is: The Messenger of Allah (peace and blessings be upon him) said: "Whoever says at the beginning of his day or the beginning of his night: In the name of Allah, with whose name nothing on earth or in heaven can cause harm, and He is the All-Hearing, the All-Knowing, nothing will harm him on that day or that night."
Note / Clarification: Abu Dawud (in the chain) is Sulayman bin Dawud al-Tayalisi.

Reference / Source: Al-Dulabi recorded it in "al-Kuna" (55) and Ibn Asakir (6/149) via Dawud bin Amr al-Dabbi; Ibn Mandah in "Fath al-Bab" (4137) via Marwan bin Muhammad al-Tatari; and Ibn Asakir (39/13) via Sa'd bin Abd al-Hamid and Surayj bin al-Nu'man; all four from Abd al-Rahman bin Abi al-Zinad, with this chain.

Note / Clarification: The aforementioned hadith is recorded in Musnad Ahmad, the four Sunan and Sahih Ibn Hibban, and it has also passed with the author (al-Hakim) under no. (1916), but none of them mentioned Uthman's kunyah in their narration; so here we have confined ourselves to the narration in which the kunyah is mentioned, since that is the author's aim here.