If our baby is a little boy and we want to have him circumcised in the hospital can the ceremony of a bris still be held or would we have a baby naming?
A bris can most certainly be held in a hospital, though very few are these days. But remember that "bris" and circumcision are not synonymous. I'll explain:
"Bris" means "covenant." At a bris, the boy is brought into the covenant between God and the Jewish People, in fulfillment of the command given by God to Abraham:
"On your part, you shall keep My covenant, you and your descendants throughout their generations. This is My covenant which you shall keep between Me and you and your children after you: every male among you shall be circumcised. You shall be circumcised in the flesh of your foreskin, and it shall be a sign of the covenant between Me and you. He that is eight days old shall be circumcised, every male throughout your generations...." - Genesis 17:9-12.
The circumcision is a sign of the covenant, a "membership badge" if you will. What we call the "bris" (Bris Milah - Covenant of Circumcision) is the religious ceremony in which the child is brought into the covenant community by means of the circumcision and the accompanying blessings, prayers which put the "medical" procedure into a religious context. Then, as a member of the covenant community, the boy is given a Hebrew name, linking him to his Jewish family and to Jewish history.
An authentic bris is done on the eighth day, as prescribed in the Torah. (One of the reasons for this which I like has to do with the child reliving the original 7 days of creation in which God was the creative force. Then, on the 8th day, human beings take initiative and "complete" God's creation.)
Doing the bris on the eighth day in the hospital involves going back into the hospital. Many people believe that hospitals and doctors are more sanitary and safer. Depending on where you live, if you have an experienced mohel (ritual circumcisor), then the likelihood is that a bris done in your home would be no less safe or sanitary than in a hospital. You may live in an area which is fortunate to have a "Reform mohel." Most of these are doctors or nurses who have been trained in the rituals of the bris.
Finally, my sense is that if a child has already been circumcised but has not had a bris, most Reform rabbis would still do a ceremony bringing the child into the covenant and giving him a Hebrew name.