A good chunk of a teacher’s job is to build appropriate relationships with your students. Students don’t want to learn from someone they dislike, and you have significantly better learning outcomes when the students feel safe, accepted, and cared about. Appropriate nicknames, like Tim for Timothy, help in that relationship building. I don’t know what your position is at that school, but Wisconsin teachers are literally taught stuff like this in college so that we know how to manage a classroom with the best learning outcomes and the fewest number of behavioral disruptions. We are taught how to keep those relationships appropriate and healthy, although much of that is just common sense.
Yes, you should separate work and home life for both your own sanity and for modeling good boundaries and work-life balance. But that doesn’t mean you have to drop your decency at the door. At the end of the day, the goal is learning, and not being a douche is one of the easiest ways to get to that goal.
Extracurricular activities are an extension of these same principles, not an exception or something with a different set of standards. I think you might be mixing up appropriate relationship building with inappropriate fraternizing, and I’m concerned that you are having difficulty finding that line.