Instead of just selecting the name and marking it as an index entry (by pressing ALT+SHIFT+X), you need to adjust the name to have the last name first. (e.g. Smith, John)
This can either be done in the dialog that appears after pressing ALT+SHIFT+X, ...
or by directly inserting a field code like this: Press CTRL+F9 to insert an empty field, then, inside the fielt enter the code "XE", followed by the text of the index entry, e.g. { XE "Smith, John" }
To quickly edit all fields you already have created, display field codes, then use the "browse by fields" function below the vertical scroll bar.