Can one classify Herpes based on the area in which it develops?

Yes, Herpes can be classified based on where the lesions or Herpes Virus is present:

Herpetic Gingivostomatitis presents itself on the gums of the mouth
Herpes Genitalis presents itself on and around the male or female genitalia
Herpes Labialis presents itself on the lips or oral mucosa
A Herpes Gladiatorum or Herpetic Whitlow presents itself on the ends of the fingers, just above the nail bed

Herpes Viral Meningitis or Herpes Viral Meningitis is present in the brain.