Hi @Kathleen470 :
I have had similar issues with guests over the last year or so. Given the time frame, I suggest that you follow the advice shared by @Yvonne191 .
Should you encounter these concerns in the future, here are some methods that I have tried:
1) For guests wanting to use e-mail, I explain that Airbnb requires that communication be via their message interface, but I will use both. Any correspondence that I receive from the guest via e-mail, I parrot back (copy and repeat) using the Airbnb interface so everyone is aware of what is being discussed.
2) Guests are required to provide the full names of all people staying overnight. I must receive this information prior to their receiving check-in information. If I don't hear from them by the morning of arrival, a text message is sent to the phone number on file. Usually, that resolves the matter. Otherwise, I would contact Airbnb customer service and ask them to follow up (haven't had to do this so far).
3) Finally, if I am still unsure about the guests' identity, I will send the check-in message WITHOUT the door code and explain that they will receive it when they arrive and show me their valid photo ID (driver's license, passport, state ID).
Avoid allowing any guest access to your rental until you feel comfortable with their identity. It is easier to stop them initially than trying to get them out later.