lots of misinformation here. You never physically sign the green book. There are two forms that need to be filled out as well as a copy of the seller's ID and if they're a foreigner they will need copies of their passport as well as their visa and their TM 30. Under the new rules if you do not change the name within 30 days they are starting to fine you start at 200 baht
I've always paid cash without an issue. At some point to register it in your name they will need a copy of your passport as well as a residency certificate but it's not needed at the time of deposit