Could I reserve a table under the name John Smith?

Meaning

Can I make a reservation in the name of John Smith?

Examples

• John: Hello, I'd like to dine in.
• Alice: Certainly, sir. <b>Could I reserve a table under the name John Smith?</b>
• John: Yes, please. For two people.
• Alice: Okay, and what time? <b>Could I reserve a table under the name John Smith</b> for 7 pm?