'your teacher Judy' is a phrase, but 'Your teacher is Judy.' is a sentence.
so let us say: if you have the formation معلمتُكَ جودي سعيدةٌ (Your teacher Judy is happy.) - it is a sentence. So in this case it translates to 'your teacher Judy'
But if you just say: معلمتُكَ جودي. Then it becomes an independent sentence meaning 'Your teacher is Judy.'
However, it is more common to use this formation as a phrase than as a sentence. A better sentence for 'Your teacher is Judy' would be: معلمتُكَ هيَ جودي. (literal translation: 'your teacher - she is Judy')