Naming the Child is the Right of the Father and Consulting the Mother is Preferred

Question :

Allah, Most Glorified, Most High has blessed me with a daughter and I wanted to name her, but her mother wanted to give her another name, so I suggested to her that we draw lots for the two names and name her according to the result of the draw. Is this Al-Azlam, and if it is, then how can we settle this conflict? And is naming the child the right of the father alone? Advise us and may Allah reward you with goodness.

Answer:

Drawing lots in such matters as this is a lawful thing, because it is a solution to disagreement and reconciliation of the souls. The Prophet made use of it in many matters, and if he intended to go on a journey, he would select one of his wives by drawing lots, and whichever one's arrow was drawn by him, he would take her with him. When a man was advised to free some of his slaves and he had only six and no others the Prophet drew lots among them, then he freed two and kept four as slaves.

Naming the child is the right of the father, but it is preferred to consult the mother in the matter, in order to make her happy and soften her heart. It is legislated for both of them to choose good names and to refrain from names which are disliked. It is not permissible when naming a child to use names which involve being a worshipper to other than Allah, such as 'Abdun-Nabi (the worshipper of the Prophet), 'Abdul-Ka'bah (the worshipper of the Ka'bah), "Abdul-Husain and the like. This is because all are creatures of Allah, Most Glorified, so it is not permissible to make someone a worshipper of another besides Him. And the famous scholar, Abu Muhammad Ibn Hazm has reported that there is unanimity among the scholars on the matter of naming someone as a worshipper of other than Allah, except for the name 'Abdul-Muttalib, for the Prophet approved of this name for some of the Companions may Allah be pleased with all of them. And Allah is the Granter of success.

Source:
Ibn Baz
Fatawa Islamiyah, Vol. 5 Pages 385-386