Q. Do you put professor full name on definition essay on the header?

The type of essay matters less than what style guide you're supposed to follow:

• MLA: last name only (e.g. Professor Weatherwax)
• APA: full name (e.g. Dr. Esme Weatherwax)
• Chicago: does not include instructor name on the title page

And of course, if your professor has provided you an example or template that is different from the above, go with that.

If they didn't give you any guidance at all in the assignment:

1. Check the syllabus to see if a blanket statement is mentioned there.
2. Ask your instructor if they have a preference! If they never mention one, they may just prefer you use whatever you're most comfortable with.
3. Your English and other humanities classes will tend to use MLA style. If it's a social science (like psychology or economics), use APA.