The easiest way to do so is create a formula field that translates Record Type ID into Record Type Name, something like:
IF(RecordTypeId = "yourrecordtypeid1", "RTName1",
IF(RecordTypeId = "yourrecordtypeid2", "RTName2",
NULL))
Make sure to add new record types to that formula (if you create new ones), and to give the Lead / contact formula field the same names.
Itay