One mean teacher name could be 'Mr. Grump'. It gives the impression of a grouchy and unkind teacher. Another option is 'Miss Scowl', which implies that she is always frowning and not very pleasant. 'Professor Stern' also works as it shows a strict and perhaps mean - spirited teacher.
In the traditional Christmas story, there isn't a specific mention of a 'teacher' in the sense we typically think of in modern educational terms. The main characters are Jesus, Mary, Joseph, the shepherds, and the wise men. None of these are teachers in a classroom sense.
Miss Garcia. She is a young and enthusiastic teacher, full of new teaching ideas, which makes the class very interesting. For example, she might organize outdoor study trips to let students learn in nature.
Miss Green. It gives an impression of freshness and nature, like a new start in learning. Also, Mr. Brown. Brown is a common and warm color, representing stability and reliability which are good traits for a teacher.