Is the name "Rancy" forbidden or unlawful according to Islamic law, and is naming a daughter this name, with the father's insistence on calling her "Maryam," considered disobedience to the father or prioritizing the wife's desire?

Naming the newborn is the right of the father, then the grandfather. A son naming his child without his father's approval may be considered an act of disobedience if it causes his father significant harm according to custom. One can apologize to the father and strive to please him. The name "Alan" is not forbidden, but it is preferable to avoid naming with foreign names.