A name check is a check, made before a bank transfer is sent, that the name the payer has entered matches the name on the recipient's account, and the best-known service of this kind is described in full under Confirmation of Payee. "Name check" is the informal, generic phrase, while Confirmation of Payee is the name of the UK scheme that popularised the idea.
When a payer enters a recipient's name and account details, the payer's bank asks the recipient's bank whether the name matches. The answer is usually a match, a close match with the correct name suggested, or no match, and the payer can then decide whether to go ahead. Name checks help prevent misdirected payments and authorised push payment fraud, in which a fraudster persuades a victim to pay an account the fraudster controls.
Similar services exist elsewhere under other names. In the European Union, the Instant Payments Regulation requires Verification of Payee for euro credit transfers. The phrase "name check" can also mean screening a customer's name against sanctions lists, which is a separate process covered under watchlist screening.