If you’ve just met someone new in Italy, one of the first things you’ll want to find out in order to avoid an embarrassing situation in the future is their name!
The most common way to ask What is your name? in Italian in an informal situation is Come ti chiami? which literally translates as What do you call yourself?
If you are talking to someone who is a) much older than you, b) of a higher status, or c) a stranger, the polite form (Lei) come si chiama? is preferred.