the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
Islamic Law does not specify that the father's parents must name the child or that the child must be given any specific name. These are purely customary matters. There is no inherent obligation.
If the parents of either the husband or the wife, for cultural reasons, would take deep and serious offense to certain naming decisions, then it would generally be best to comply with that specific parent's wishes and avoid a dispute.
Exceptions to this would be when the name in question would somehow be to the disadvantage of the child later on in life, since the child's future interests take precedence in this regard.
The Prophet (peace be upon him) said: “There must neither be harm nor the imposition of harm.” [Sunan al-Daraqutnî (3/77), al-Mustadrak (2/57), and Sunan al-Bayhaqî (6/69)]
The child's welfare is paramount, and the child should not be given a name that would prove limiting in his or her future life, regardless of the sentiments of some of the child's relatives.
In the case of a dispute between various interested parties in the matter – like a clash of customs between the woman's family and the man's family regarding naming rights – the matter should be determined by some sort of local arbitration to restore the peace and harmony between the families and cultures.
Such matters can sometimes be sensitive, especially when the families come from different cultural backgrounds.
In circumstances that are less sensitive, the husband and wife should simply discuss the matter among themselves like two reasonable adults and come to some sort of agreement or compromise. Picking out the name of a child should ideally be a cause of joy and shared pleasure for the prospective parents.
And Allah knows best.
Source: Islam Today