This look up field will always take user id.
Probable options,You can add a formula field on the form which will populate/show full name once the record is saved.
Example: have user look up field call Select Emp manager to populate the name put a formula field.
Full name Select_Emp_Manager__r.FirstName&" "&Select_Emp_Manager__r.LastName
You can also include the full name in the popup > customize > user object > filed sets> column headers> add the column full name