In gatherings of men, in social life and the interchange of words and deeds, some men are thought to be obsequious, viz. those who to give pleasure praise everything and never oppose, but think it their duty 'to give no pain to the people they meet'; while those who, on the contrary, oppose everything and care not a whit about giving pain are called churlish and contentious. That the states we have named are culpable is plain enough, and that the middle state is laudable- that in virtue of which a man will put up with, and will resent, the right things and in the right way; but no name has been assigned to it, though it most resembles friendship. For the man who corresponds to this middle state is very much what, with affection added, we call a good friend. But the state in question differs from friendship in that it implies no passion or affection for one's associates; since it is not by reason of loving or hating that such a man takes everything in the right way, but by being a man of a certain kind. For he will behave so alike towards those he knows and those he does not know, towards intimates and those who are not so, except that in each of these cases he will behave as is befitting; for it is not proper to have the same care for intimates and for strangers, nor again is it the same conditions that make it right to give pain to them.
While in NE 4.6 (and 2.7) this particular virtue isn't given a name there are various categorisations in EE 2.3 and 3.7 that are clearly related. The different texts divide things up in different ways. Also, Magna Moralia 1.27-32 has a tidy (perhaps too tidy) set of related social virtues, including being correctly indignant (nemesis) and being appropriately witty (eutrapelia). The most likely candidate for the name of what he is discussing in 4.6 is something like 'semnotēs'.Now we have said generally that he will associate with people in the right way; but it is by reference to what is honourable and expedient that he will aim at not giving pain or at contributing pleasure. For he seems to be concerned with the pleasures and pains of social life; and wherever it is not honourable, or is harmful, for him to contribute pleasure, he will refuse, and will choose rather to give pain; also if his acquiescence in another's action would bring disgrace, and that in a high degree, or injury, on that other, while his opposition brings a little pain, he will not acquiesce but will decline. He will associate differently with people in high station and with ordinary people, with closer and more distant acquaintances, and so too with regard to all other differences, rendering to each class what is befitting, and while for its own sake he chooses to contribute pleasure, and avoids the giving of pain, he will be guided by the consequences, if these are greater, i.e. honour and expediency. For the sake of a great future pleasure, too, he will inflict small pains.
The man who attains the mean, then, is such as we have described, but has not received a name; of those who contribute pleasure, the man who aims at being pleasant with no ulterior object is obsequious, but the man who does so in order that he may get some advantage in the direction of money or the things that money buys is a flatterer; while the man who quarrels with everything is, as has been said, churlish and contentious. And the extremes seem to be contradictory to each other because the mean is without a name.
In any case, the surrounding discussion makes clear that in these social dealings Aristotle thinks that there are two important factors: one is a question of truthfulness and sincerity in what we say and do and another is the question of causing pleasure or pain to the recipient or recipients of the words or actions. That seems right.
I think this contains some important and suggestive points. It's important that what is being discussed here is not confused with being 'friendly' or 'polite'; what matters is not the form of words that is used but the intention and purpose of the agent who is using them in a given social setting with a particular interlocutor. There are no set 'rules' that govern the way that a view can or should be expressed; what matters is why you are saying what you are saying, when, and to whom. The virtue being discussed here concerns dealings with people who are not friends (or, we might add, dealing with people who are friends but not qua friends, and so also colleagues, fellow academics etc.) Sometimes the right way to talk is to be critical and to cause offence but giving offence per se is not something worth aiming for.
Also important is something Aristotle mentions explicitly a little later in 4.8: that it is important not only to speak in the right way but also to listen in the right way too (1127b33-1128a2).