Before I finally finished the doctorate, my syllabus said, "Call me Bob or Mr. Brown, whichever is more comfortable for you. but not 'doctor' or 'professor.'" Other than that, I didn't worry about it with students. Faculty all call each other by first names anyway, so it never came up in that context. (Now the syllabus says, "Call me Bob or Dr. Brown, whichever is more comfortable for you.")
My professional correspondence (email and postal mail) includes both my degree and my academic rank, so anyone corresponding with me has the correct information whether they need it nor not.
Outside school, I corrected those with whom I expected a long acquaintance, such as a new dentist, by saying, "Please call me Bob." If that didn't work, I added that I did not hold a doctorate. For everyone else, I ignored it.
In my institution and many like it, "professor" is used as a courtesy title by students for faculty who do not hold the doctorate, and less as a title of academic rank. How one reacts to "professor" will depend on local custom. Whether to correct those who call you professor depends on how it's used where you are. If one is a faculty member and "professor" is used as a courtesy, no correction is necessary.
I am reminded of a novel in which a character addressed as "doctor" says, "Oh, no! Not 'doctor." I'm only a humble F.R.C.S."