The baby should be named no later than the seventh day. On that day, the aqeeqah is performed (animal is slaughtered on his behalf to show gratitude to Allah), his head is shaven, he is circumcised, and given a name.

It should also be noted that if the baby is a boy, two sheep is slaughtered, and if a girl only one sheep. The head of the baby should be smeared with some saffron.

I would also like to add that the custom of some Muslims to circumcise the boys at age seven or eight years is totally against the Sunnah and is a rejected custom. The baby boy should be circumcised on the seventh day after being born, as circumcision is from the fitrah and required for ritual purity.