do all folders, documents on the desktop transfer to a new mac

If you use Migration Assistant to transfer your data from an old Mac to a new one, or from a Time Machine backup, then yes, all folders and documents on the user's desktop will be transferred.

Move your content to a new Mac - Apple Support

When you set up your new Mac, if your plan is to transfer the User account(s) from the old Mac or its TM backup, I suggest you start with a user account that does not have the same name as the user account you will transfer from the old Mac. It just helps to keep things clear and separate when you migrate the old account. Once your data migration is complete, you would continue to use the migrated user account, and you would also have a new, second admin account available for troubleshooting if necessary. Even if you never need to use it, it's good to have in place.