Hi @Jen15 When Airbnb gives a Verified ID badge to a host or a guest, it means that the person has provided enough identification including a governemental identification such as a driver's license or passport among other things. Here's a link that explains more:
https://www.airbnb.com/help/article/450/what-is-verified-id
I've tried finding people on Facebook, but without a last name (at least until I have a confirmed booking) sometimes it is not possible. Their profile name on Airbnb might be Suzy while their Facebook name might be Suzanne. Or they are using a maiden name, not a married name. I know some hosts who do a Google image search on their profile picture. Sometimes people use the same picture for Facebook.
If Airbnb has verified their ID you can be reasonably sure the person is who they say they are.
I require Verified ID for anyone wishing to make a reservation with me. It's under Reservation Requirements just to the left of wher you see Calendar and More when you select Manage Listing.
I wouldn't worry about double checking people's identity. If the person has Verified ID, Airbnb has already done it.
Hope this puts you at ease!