What is your name?
However, depending on the context and the speaker's personality, they might use slightly different phrasing:
* May I ask your name? (more formal)
* Could you tell me your name? (polite)
* What's your name? (casual)
* Your name is? (short and direct)
It's important to note that these variations are not exclusive to British English and can be used in other English-speaking regions as well.