@Debbie106
What you should take with you for the future is:
When a guest goes against Airbnb principles, they are the ones at fault.
Yes, you should make them aware of this to cancel.
If they don't, then no, it's not your problem to cancel.
BUT you should call Airbnb and tell them about the booking going against Terms of Service.
They have to undo the booking.
If you simply cancel the system software registers that as host cancellation because it can't read minds.
So in these kind of precarious situations, you need to do it by involving Airbnb.
Help minimize your guest risk yourself:
Make sure you get the full name of the guest booking. Otherwise ask them for it.
If the reservation is for more than one person ask for full names of all guests.
Mention in your house rules somewhere that there will be ID checks on arrival.
Keep a registry like a hotel and make sure you include ID nos.
In the case of somebody arriving with a different name, you need to tell them "We have a problem, because booking is not for you and I'm not covered by Airbnb for 3rd party bookings". Don't even let them into the room. In their presence you call Airbnb, the no. of which I'm sure you have on speed dial. They will have to solve the problem since that booking will be against their own TOS.