If a PhD student who behaves badly, e.g being rude to other PhD students/staffs, distracting people in the same office by talking loudly or making noise..., should his/her supervisor do anything to deal with that student? If the answer is yes, what should a supervisor do?
There's obviously no universally accepted policy here (e.g., there are labs where brashness unfortunately starts with the principal investigators). You also need to be careful about what is meant and perceived as rude, as it is, partly, an artifact of culture (e.g. I've witnessed Japanese managers fake sleeping during business meetings, which I would be inclined to perceive as negligent or rude, but apparently expresses ritualized trust in their underlings acting for them). That said, and assuming there is confirmed rudeness, here is how I would handle this.
There should be a zero tolerance policy for rudeness towards staff as it is likely abuse of power, or perceived status. If you experience such rudeness towards other students during meetings, etc., I'd call the offender out as it happens ("There's no need for (X). We are all working together/(Y) didn't mean to imply this."); if during inter-student conversations you happen to witness, I'd first confirm with the person on the receiving end if they share your perception ("Is everything all right? You feel comfortable in our lab? (...)"), if the case is not blatantly obvious. In all cases that warrant action, I'd call the offending student for a personal meeting, in which you could outline that you prefer a more mellow lab, with suggestions how to better handle what happened. If this is a meeting with a repeat offender, be more forceful and tell them that they continue to be out of line, and that this has to stop.
If you are personally disturbed by the noise level, you should say so - it's your lab. However, if you'd rather provide a quieter lab for your students, this is a common workplace problem with few known satisfying solutions. Here is an old question discussing the issue. The main problem is that some people prefer to talk while at work, others prefer to focus; if you take one side, you are likely to annoy the other. I find loud talkers rude and inconsiderate, but have never managed to change my surroundings in a lasting way.
Necessary note: I'm a PhD student. My experience in these matters is zero, and this is merely opinion.
With regards to distracting others, that isn't something to take lightly. However, as long as the others regularly tell them to be quiet, they'll hopefully get the hint eventually. A lot of the time, people just don't know that they're being a distraction. There are also some circumstances where they don't even realise they're being rude to others. Self-awareness might not be strong with this one.
Alternatively, it could be an attitude issue. If they acknowledge their rudeness and habit of distraction, or if they get very defensive about it when asked, I think that it's safe to say that they don't understand their position. Perhaps they believe they are more important (or less disposable...) than they truly are, or maybe they want to be important and see placing themselves on a pedestal as a way of achieving that (I think we've all met someone like that).
There are a lot of "if"s and "but"s surrounding this. Have you approached them about it at all? Has anyone even said anything to them? I would say that it's your role (if not your job description) as a supervisor to steer them towards becoming a better researcher as a whole. Their attitude towards other researchers, as well as their idea of their conduct whilst doing their own research, is a key part of this, so IMHO it would be your responsibility to give it a shot, at least.
The method? Well, when my supervisor wants a non-academic discussion (from "here's something interesting Im working on, do you want to join in?" to "I could do with a draft of that paper ASAP"), it's always a cup of tea and an informal chat, so that's a tactic I can vouch for. In your case, nothing intense and nothing to get their defences up if they're that way inclined. If things dont improve, repeat. If things don't improve THEN, make that water and a more formal discussion. If things don't improve, they have made their attitude towards your advice clear, and you should take matters out of your hands and up the chain of command, so to speak.
(Note, I don't think it's fair to assume from the question whether the OP is the supervisor in this scenario.)
If I imagine a student being rude to other PhD students, and distracting people in a group office by talking loudly or making noise, I would say that these interpersonal problems may be solvable by working things out at the student level. An I-message like this might do the trick:
Clark, you have one of those nice, big booming voices that's incredibly helpful in a crowded room. But when I'm meeting with a student in the class I TA for, I have trouble hearing, and making myself understood, over your conversation. Also, when I'm concentrating on my own work, sometimes I end up typing what I hear you saying -- it's so compelling. So I was wondering if you could take your chats down to the coffee room?
If a student is consistently rude to a secretary or a technician, the secretary or technician will probably give that student "least favored student" status, and things may work themselves out naturally.
On the other hand, the problem may be beyond the above.
Nevertheless, some supervisors aren't comfortable dealing with this kind of problem. Let's face it, not everybody is good at research in their field and managing human resources.
Fortunately, there are structures in place in departments that can be asked for assistance if need be.