An employee form template would normally ask for the name of the person, his department or his position title. Those information are necessary so that from the list of many employees of the company, each one may be identified from the other. Part of the template would be the complete address of the employee.
The social security number will be part of the template. It will provide the company everything it has to know about the employee. If he has an outstanding warrant of arrest from the police, if he is an outstanding debt, what responsibility he has, what violations he did, etc.