Custom registrations fields not saving data

I have added a number of custom registration fields to the registration form following the instructions in the documentation. However, a new registrations first name and last name does not appear in the WordPress user database when I edit the user from the back-end, but when I am logged in as that user and I edit the profile, the data entered when the user registered is there and can be edited.

For a user that already exists, the problem is the opposite. Their details appear in the back-end, but when they try to edit their information while logged in, the data does not appear.

I have also got fields such as Job Title and Company, which are not fields that currently exist in the WordPress database. Is there a way I can add these fields to the database?

Thanks in advance.