* Quel est votre nom ? (What is your name?)
Informal:
* Comment t'appelles-tu ? (What is your name?)
* C'est quoi ton nom ? (What is your name?)
More friendly:
* Tu t'appelles comment ? (What's your name?)
* Tu peux me dire ton nom ? (Can you tell me your name?)
You can also use the phrase "Enchanté(e)" (Nice to meet you) after they tell you their name.