The naming ceremony was a ritual observed on the planet Kataan shortly after the birth of a newborn baby.
The parents would decide on the name for a child, sometimes naming the baby after a deceased loved one, and announce it to gathered friends. The naming was followed by a party with a large buffet.
In 2368, while experiencing the life of Kamin, Jean-Luc Picard and Eline recalled their daughter Meribor's naming ceremony just after Batai's was held. He remembered being afraid he would drop her. (TNG: "The Inner Light")