Personally I don't take long term bookings @Shelby64 , but as you accept them, presume it is something that works for you.
I would make the following points;
1. Ask for the full names of all those who are booked to stay
2. Query why the name on the account name is different from the one they booked under
3. I believe in the US you have legal issues for guests staying over a month in terms of your tenancy laws - don't you need to have a tenancy contract in addition to Airbnb?
4. It is normal if you are immigrating to a country to need a mailing address for bank accounts, doctors, schools, official records, work etc
5. Be honest say you are hesitant about accepting a long term booking from someone who is knew to Airbnb. Ask them about plans for their stay, where they are working, why they have chosen your location etc