1) Naming A Boy– It is well known that the custom is to name the boy at the Bris. This custom is sourced in the Rishonim. (Siddur Ri Ben Yakar) The reason for this is that only after the baby is in his perfected state, after the removal of the orlah (foreskin), is the baby prepared to receive his Jewish name. (Chesed l’Avraham 2:52)

2) The poskim discuss what to do if a child is ill and will not be able to have the bris on time at 8 days: A) The Sefer Chemudei Daniel is of the opinion that if a child is ill and will not have a bris for weeks, one may give him a name before the bris. According to the Chamudei Daniel one should name the baby before he is 8 days old, while the Sefer Kores Bris (page 25) maintains one should name before the bris, but after the baby is 8 days old. Indeed, there were rabbanim who endorsed naming an ill baby before the bris so that the baby will have a name that others can use when davening for his recovery. Rav Moshe Feinstein zt”l and the Satmar Rebbe zt”l are also cited as advising one to give an ill child a name, even before the bris. (Refer to Kovetz Asia page 244) B) Harav Shach zt”l is cited as ruling that one should only name the baby before the bris if the baby is in a life threatening situation. However, if the bris is postponed because the baby’s bilirubin levels are high, however, the baby is not in a life threatening situation, one should not name the baby before the bris. C) The Steipler Gaon zt”l is cited as ruling that one should never name the baby before the bris. According to the Steipler Gaon zt”l if one wishes to daven for the baby one would pray for “tinok (child) ben plonis.”