Naming Day was the day on which male Ferengi were formally introduced to the world outside their family and one of the first opportunities for a young Ferengi to acquire property or make a profit. It was one of the few Ferengi traditions that involved the giving of gifts.
On Rom's Naming Day, his brother Quark replaced his gifts with old vegetables and sold the gifts for a profit. In 2370, mentioning this incident specifically, Rom complained about his difficult childhood to Martus Mazur, who wasn't interested in the least. (DS9: "Rivals")