There are many customs in Judaism for before after and during the Brit Milah.
Many have a custom to stay awake the night prior to the brit to protect the baby from evil spirits.
There is a custom to put a special sign next to the baby’s head to protect it from evil spirits.
There is a custom to have the Brit Milah in the house of the family of the baby.
Many have the custom of lighting candles in the room of the brit.
Some have the custom of singing the psalm 100.
Thaere is a custom to put a sefer (jewish book) next to the baby to protect it.
During the bris there is a custom to give the baby to drink from the wine of the ceremony.
There many customs regarding the giving of a Jewish name. To learn more click here.