1) Please be sure that you have correctly configured "Content of booking fields data" form at the Booking > Settings > Form page.
For example, if you are having in the booking form configuration like this:
Last Name (required): [text* secondname]
so then at the "Content of booking fields data" form you need to have configuration like this:
Last Name: [secondname]
Please use shortcode generator at the right side of the Booking > Settings > Form page for the fast and correct creation of booking form fields.
2) Also in some old premium versions of Booking Calendar together with latest update of WordPress possible issue that all entering fields in booking form are blank.
In this case you need to update your version of booking calendar to latest update or rollback your WordPress version.
You can request the new update of Booking Calendar on this page.
After installing update, please make fully NEW bookings to test that booking details is saving correctly.