The right to the personal name represents the most important expression of a personal identity, as well as an absolute subjective right of every individual. Furthermore, the individual is, through the personal name, distinguished in the known and social context, and it is also the means through which the state identifies its subjects. Without the existence of the personal name, the life within a community would be unimaginable, which means that this type of individualization is as old as the very human society. Nevertheless, through time, the means of such an individualization have been changed. Today, in Republic of Serbia, the personal name consists of a surname by which the belonging to a certain family community is expressed, and a name through which he/she is individualized within that community. The question of a personal name in our country is regulated by the Family Law and it is guaranteed by the Constitution. Given the importance of the personal name, the aim of this paper will be to demonstrate the important questions pertaining to the personal name, as well as the Family Law norms, by which it is regulated within the lawful context of Republic of Serbia.