Add one more text field to your table and give it an auto-entered calculation such as:
FirstName & LastName.
Clear the do not replace existing value check box.
Select a unique values validation option for this field and it will catch instances where the combined first and last names are not unique.
I created a new field named c_FullName. I placed a checkmark in Calculated Value and specify it as FirstName & LastName. I cleared the check from do not replace existing value check box and placed a check mark in Unique Value. But when I enter in the same First Name and Last Name in the layout nothing happens.
I use this all the time and it works. What data typeis c_FulName? It should be a text field. c_FullName, FirstName, LastName all need to be defined in the same table. It won't update properly if the name fields are from a different table.
But the most likely issue is that you have existing records created before you added this field. A newly added field with an auto-entered calculation setting will not have a value in it for the existing records. It will enter a value only for new records added afterwards.
See this thread for a slick way to get your existing records to update this field: Updating values in auto-enter calc fields without using Replace Field Contents