大名 contrasts with 小名 (xiǎomíng, childhood nickname). Asking someone's 大名 is a polite, slightly formal way to ask their name. 久仰大名 is a classic polite greeting meaning 'I've heard so much about you.'
culture
In traditional Chinese naming, a person had a 大名 (formal name used in official contexts) and a 小名 (pet name used by family). This distinction persists in modern Chinese culture.