The root of the problem is of course that authority works very differently in schools than in universities and the workplace. Young undergraduates are still in the process of adjusting to the new environment, and in large groups they tend to feel strong and carry over the behaviour they have grown up with. In the eyes of the average high-school student, actual subject knowledge is almost dispensable, but a teacher who doesn't know the tricks of the trade is a weak teacher who is asking to be trampled upon.
I haven't tried this yet as I haven't been in a comparable situation, but based on some experience teaching both at school and university level, I suggest the following in conjunction with other techniques:
In each class with a noise problem, ask one student for his or her name. Ideally this should be one of the students who were noisy, but this is not necessary. In case of any escalation, ask that student (and possibly one or two others, but no more) to see you at the end of the class. Do not announce any consequences or threats whatsoever. The only real consequence will be that you will remember the student's name and will not forget it until the end of the semester.
If one of the students whose names you know is noisy, call that student by name. If someone in the neighbourhood of a student you know is noisy, still call the one whose name you already know. Only if you are absolutely sure that student was quiet, call one who you think was noisy, identifying them as, e.g., "the one in blue to the right of John Doe".
Picking out a student even if you are not sure it's the right one is obviously not fair, but it's often necessary in this kind of environment, and that's why experienced high-school-level teachers often resort to this method. Announcing that you are going to have a word with a student later makes the students think about what could be the worst thing that might happen. Nobody wants to be swapped in for that student. Since most students have no idea of how restricted your options are, that is much more effective than any real threat, and you are not going to lose credibility if nothing happens. Actual threats or announced consequences are less effective, you risk the reaction "So cheap? I want that too so I appear equally cool before the others!", you risk losing all credibility if nothing happens, and it's often a lot of work to carry out whatever it is you announced.
Demonstrating that you remember the the names of (likely) noisy students is a similar strategy. Students will think of all sorts of ways (many of which would never occur to you) how you might manipulate the grades of those students you appear to have taken a dislike to. They don't know that their fears are unfounded before exams are over. (If you need to reinforce this fear, you might tell them sincerely but not too convincingly that you will do no such thing.)