It is said to have been a practice of picking up mochi and a piece of vegetable together to eat, which was for good luck with a pun: 'mochi ageru' (raise a mochi = win), and 'na' (vegetable, or 'name' in Japanese) to make it 'win one's name.'
餅と菜を一緒に取り上げて食べるのが習わしで、「名（＝菜）を持ち（＝餅）上げる」という縁起担ぎだったという（上記の習わしが武家社会一般の作法だったという説は、誤伝による俗説）。