Learn English – “How to know” vs. “How to know”

Yes, "you" can be either singular or plural.

The conventional way to ask this question would be: "What are your names?" If you were asking only one person for his name you would day, "What is your name?"

(There is a small possible ambiguity if the person has more than one name. Like if someone was a criminal who regularly used fake names, the policeman might ask him, "Okay, so what are ALL your names?" Perhaps I should clarify that while people regularly have first, middle, and last names, we still refer to all of this as "your name". People say, "My name is Fred Smith", not "My names are Fred Smith.")

I'm not sure why you said "actual names" in your examples. The word "actual" would only be meaningful in the sentence if it is necessary to contrast with some non-actual name. I guess if you were asking a group of actors, you might want to make clear that you mean their real names and not the names of their characters in the show. Or if there was a possible ambiguity whether you meant their log-on id's to the computer system versus their real names. But normally, you just say "name".

As to your examples:

1.What are the actual names of yours?

Grammatically correct, I suppose, but awkward. A fluent speaker would be more likely to say, "What are your actual names?"

2.What are the actual names of you all?

Acceptable for casual speech, especially in the southern U.S., but would likely be questioned if used in formal writing.

3.What are the actual names of your?

No. "Your" is a possessive and does not fit here. It is an adjective with no noun to modify. You could say, "What are the actual names of your friends?", etc

4.What are the actual names of you people?

Fine for casual speech, but a little awkward. Probably would not be used in formal speech. Also, the phrase "you people" can be considered rude. It implies that they are members of a class that is different from yours and presumably inferior. I'd avoid this phrase except when you want to indicate anger or disdain. "You people get out of here!" Or, "I'm tired of putting up with you people."

5.What are the actual names of all of you?

That's perfectly good and grammatical. It's more long-winded than necessary, which may or may not be a bad thing.

Your can indicate something specific that the people in the conversation are aware of or have a reference to, at least in casual conversation. The OALD entry for your includes

3. (informal) used to show that somebody/something is well known or often talked about

This is your typical English pub.
(ironic, disapproving) You and your bright ideas!

Macmillan's entry has a similar sense:

informal used for showing that something is a typical or normal example of its type

The National Television Awards is your typical glitzy event.
This group is better than your average pop band.

Merriam-Webster offers a more forceful definition:

used with little or no meaning almost as an equivalent to the definite article the:

your typical teenager

Still, I would not use your in this sense in formal communications, and it is not interchangeable with the even in American English. It would be safer to say that your refers to someone's experience with something, and not that it is necessarily owned or associated with them. The effect of using your instead of the or another determiner is to suggest a shared knowledge or understanding of something. The effect is thus mildly ingratiating and socially leveling. My neighbor said this isn't your typical January weather to me because we both know that a forecast high of 68°F (20°C) is not normal for Washington, D.C. this time of year, and we can build a rapport based on that.