I can think of two different ways:
1 - Get an ElementType element and get FamilyName property ...
Element elemType = dbDoc.GetElement(fp.GetTypeId()); ElementType type = elemType as ElementType; string familyName = type.FamilyName;
2 - Get the built-in parameter ELEM_FAMILY_PARAM
string familyName = fp.get_Parameter(BuiltInParameter.ELEME_FAMILY_PARAM)