You should call her "Ms. [last name]" or "Mrs. [last name]" (find out from your girlfriend if her mother prefers Ms. or Mrs.--or Miss, for that matter). If she has a doctorate or is a medical doctor, you should address her as "Dr. [last name]." Only use her first name after she has invited you to do so. Many woman nowadays will offer that immediately, but the choice is hers, not yours.
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