The priest should again be invited to the home on the 8th day (remember, when counting days since birth, the day OF THE BIRTH is 1, the day after the birth is 2, etc.). On this day the child is given its Christian name. Yes, it is true, you had to put a name on the birth certificate, but the child doesn't “really” receive its name until these prayers are read. The prayers are short. The priest doesn't expect a clean house or a meal, but it is very important that these prayers be read. In Russia before the Revolution the priest often chose the name of the child rather than the parents. The child needs to have a name on the 8th day. If you haven’t chosen a name by that time (this is unusual, but not unheard of) the priest will help you (or will name the child himself).
When should the child be baptized? Certainly not later than about the 40th day after birth. The mother comes to the Church for the first time after the birth on the 40th day and prayers are read especially for her on this day. If possible, assuming good health of the baby, the baptism would ideally be done at this time.
The choosing of Godparents if very important. The Godparents should be chosen with this in mind: that at the untimely death of the parents one of the Godparents would raise the child. Also, Godparents should participate in the spiritual upbringing of the child by making sure that the parents bring the child to Church regularly. Someone may be your good friend, but at the same time not make a good Godparent. The Godparents should be of an upstanding moral character, regular churchgoers, and not living in violation of the Church’s canons. The Godparent must be an Orthodox Christian. One Godparent of the same gender as the child is mandatory, a second (of the opposite gender) is optional.