For cô gái, cô is the classifier. Cô is a noun that basically translates to "Miss" (or aunt), gái means "girl", and together it means a young girl.
Cô An, for example, means "Ms./Mrs./Aunt An". As for knowing when it means Ms./Mrs. or just Aunt, you won't know if you are an outsider to the conversation. Relationship pronouns are complex in Vietnamese.