Brit L'shem Gerut
In modern times the expression "every male among you" is taken to mean every Jewish male among you. Circumcision does not make a male child Jewish; he is Jewish if his mother is Jewish or she had converted by the time of his birth. If a baby is not Jewish, he may have a brit as the first step of conversion.
In this case, if the child is to be raised as a Jew, the ceremony is called brit l'shem gerut and parallels the brit milah so closely that most attendees will not notice the difference. Brit l'shem gerut customarily is performed on the eighth day of the boy's life, but a later date is acceptable under halacha (Jewish religious law). Brit l'shem gerut frequently is used for adoptees and when the birth results from surrogacy. While no witnesses are required for brit milah, brit l'shem gerut requires the presence of two adult Jewish witnesses who are not related to the baby.