As as general rule, "less specific" is best, particularly if you are not absolutely certain. The search will return every example that "fits" your search.
Example if you are looking for an animal named "Princess Grace", you may simply typing "Princess" in the animal name fields. This will return every example (16 animals) where "Princess" is used in any part of the name. You can further narrow your search by including other information, such as "red" in the color field or selecting a State.
If you have any questions, please contact Registrar.
