How to sign your email to students, so to avoid their immature behavior? Or how would you like to be addressed?

As a graduate TA, I went by my first name. But I thought that some students were becoming too friendly. They took things for granted (for example, asking for a homework extension every week without even bothering to make up an excuse, or showing up to my office hours and interjecting with comments meant to be funny but came out sounding obnoxious).

I will be an assistant professor next year, and I am wondering whether asking my students to call me Dr. LASTNAME would resolve some of the rudeness that I've encountered.

But how do you ask? Sign my email Dr. LASTNAME? That sounds pretentious. Should I just use initials (FL for FIRSTNAME LASTNAME)? I sign all my emails with my first name, but doing that for students is an open invitation to call them by my first name. How do people transition from a graduate TA to someone with a PhD in front of a class full of undergraduate students?

**EDIT: I have had several students be truly rude to me, but in keeping with the spirit of anonymity, I did not describe in detail what happened. But My colleagues were shocked and appalled at some of the behaviors that I have encountered.

That said, I do very well with evaluations, often nearing perfect score, and my students score well above average in multi-section calculus classes. As you might imagine, my classes are fairly well-attended with high level of  participation. Of course there are pros and cons of familiarity, but I am somewhat puzzled at this display of lack of authority in my classroom, as all of my colleagues also go by their first names. I hope this is more information.**
Like JeffE's comment, I always prefer students to call me by my first name. My male and female, Asian and white colleagues also prefer to be called by their first name. There are some exceptions where they insist on some title according to local custom for showing respect. However, I do not have the problem you describe (students expecting unreasonable things and acting in completely unprofessional ways). The reasons that I do not have to deal with these problems is because I simply do not accept them.

Actually, I am fairly strict but also fair and I always try to be open, transparent, and predictable to my students. They know if they arrive to class late, they are absent. If they submit late, they fail. They want more time, they won't get it. 

I do not see how what I allow them to call me (excluding rude names) would result in overly familiar behavior. Indeed, many of my Asian colleagues are far closer to students than I would ever allow myself to become. The ones who demand more formal forms of address are the ones who seem to get the closest with students. Perhaps this is how they remind students that they are still the teacher.

In short, student behavior is driven by your attitude towards them and you can convey a tone of seriousness in the relationship without requiring formal salutations.