I'm on FMP8 and the contact management template only shows related by last name when the "Name" radio button is checked.
This is a relationship between the Contact Management TO and the Similars TO based on a SimilarsKey calculated field.
There is a case statement in the Contact Management table field called "SimilarsKey" which references a SimilarNameKey.
If this was changed in FMP10, the change is likely (guessing here) in the definition of SimilarNameKey. Look into that field definition. In FMP8 (where it's last name only) there it is simply "=LastName".
If not, look into the SimilarsKey case statement to see how it is linking by first name OR last name.