Learn Spanish (Spain): ¿Y la vuelta?

You are exactly right! The word vuelta comes from the verb volver (to return). In a shop or restaurant, la vuelta (or sometimes the plural las vueltas) refers to the money the cashier returns to you, which is your change!

I thought the Spanish word for "change" was cambio. Can I use that instead?

Yes, you can! The word cambio (or el cambio) is also widely used and perfectly understood for money. However, in Spain, you will hear la vuelta or las vueltas used very frequently at the cash register, so it is a great everyday phrase to know.

Why is there no verb in this sentence?

In spoken Spanish, just like in English, we often drop the verb when the context is obvious. Starting a question with ¿Y...? (And...?) is a common, natural way to point out something that is missing. It is a quick way of saying "And what about the change?" without building a full sentence.