Yes it is; I would use some sort of internal mapping of the publicly displayed fields and associate them with field names.
// forms left, db field names right
$flds = array (
'fname' => 'first_name',
'lname => 'last_name'
It may very well be that you can use this array to apply to multiple tables, that is, you may have a shipping table and a customer table both containing fields first_name, last_name.
The second thing I'd do is pass the list of the table names as one of your parameters of whatever functions you use them in. Then you don't have to modify your class every time you want to change the table structure.