@Elaine116 Third-party bookings aren't allowed, but Airbnb does allow for a single account to represent multiple users (for example, @Mike-And-Jane0 who commented below), and it also allows verified users to have a pseudonym as their profile name.
If the guest is refusing to answer your questions, that's enough of a reason to consider cancelling. But if your main concern is about the profile's identity being genuine, another option would be to require guests to present an ID at check-in.
You can also disable Instant Book and screen your guests before accepting. From the guest perspective, a cancellation is a lot worse than a decline.