Polite counter for people, used in formal settings like reservations or inquiries. Compare with 何人 (なんにん), which is more casual.
See also: 名 (めい)
How many people in your party for the reservation?
参加者は何名ですか。
How many participants are there?
何名 is a more formal or polite way to ask 'how many people,' often used in business, reservations, or service settings, while 何人 is the everyday, neutral term.
Compound of 何 (なん, 'what') and 名 (めい, counter for people). The reading めい is the on'yomi of 名.