Introduction. The article discusses the features of the exercise by parents of the right and obligation to determine the name of the child and its change, which are included in the list of personal non-property rights and obligations of parents, evasion of which may lead to deprivation of parental rights. Theoretical Basis. Methods. The methodological basis of the study was philosophical methodology (dialectical method of cognition), general scientific methodology (modeling, logical analysis) and private methodology (comparative legal method, method of interpretation of law). Results. It is determined that the exercise of the right and the fulfillment of the obligation by parents to determine the name of the child takes place when registering the birth of the child. The authority of the father depends on the state of marriage with the mother of the child and the presence or absence of the will to establish paternity on a voluntary basis. In connection with the admission of registration of the birth of a child at the request of other persons, the authority of parents to determine the name of the child should be interpreted broadly. Parents should take steps to register the child’s birth with the civil registration authorities. The change of the child’s surname may take place after the registration of the child’s birth, but before the child reaches the age of sixteen. The procedure for such a change, the conditions that must be observed to change the surname, depend on a number of facts – the family legal status of the parent, the presence or absence of the will of both parents, the age of the child, the presence or absence of the consent of the child who has reached the age of ten. Discussion and Conclusion. Parents exercise the right and obligation to determine the child’s surname when registering the child’s birth with the civil registration authorities. After registering the birth of a child, a change in the child’s surname may take place if he has not reached the age of sixteen. Changing the surname of a child under the age of sixteen is the responsibility of the parents only in the event of a surname change by both parents. In cases where paternity is established on a voluntary basis, when submitting a joint application for registration of the establishment of paternity, the parents in the joint application exercise their right to determine the child’s surname, since the choice from the surnames of the parents is carried out regardless of the discretion of the law enforcement authorities. The powers of parents to change the name of the child are limited by the discretion of law enforcement authorities.