Comming from a 13 year old's point of view the informal reloationship between student and teacher is the key to success. I have 2 classes one formal, and one informal. In the informal class students (like me) achieved much higher grades.
My point?
Ask students to call you whatever they want. Just be sure to be their friend and their teacher, not just their teacher.
Unfortunately, my experiences with high school age students only tends to support the old adage that "familiarity breeds contempt." Without the boundary of formality, classroom discipline becomes untenable. While some high school students have the maturity to be on a first name basis with their teachers and still respect the teacher-student relationship, too many do not.
Here in Denmark we always call teachers by their first names. I did so in kindergarten, primary and lower secondary school, high school and university. I've never ever called a teacher by their last names. In Denmark addressing teachers or people in general by last names would be considered old-fashioned because that's how it used to be in the old days. Even the Danish prime minister is often just called by his first name by journalists.
I can comment as a student here, UK, year 13. Generally, up till the age of 16, we call our teachers by their surnames simply as a sign of deference, helping the teacher to keep control of sometimes rowdy classes. However, from the age of 16 + (yr 12 and 13), a different policy is held with most teachers.
Within lessons, as a sign of respect, we call our teachers by their last names. Outside of lessons, most of the teachers are talked about and to using their first names or nicknames. For example, the senior choir refers to the teacher who runs it by his nickname, same with the theatre and drama groups.
I think this is a great idea - by the time teenagers have reached 16 they continue in education by choice and therefore should have more priviledges.