What's the antonym of "stage name"?

I have written this before and I shall write it again.

Antonyms can only be surmised within a bi-modal phenomenon. This reasoning does not pertain to the English language alone, but to any language in the Universe. It is a basic axiom in perceiving the functioning of the Universe.

Let's illustrate with perceptions that are classified with two and only two states.

• temperatureLevel{hot, cold}
• depthLevel{deep, shallow}
• spirituality{good, evil}
• languageUsedInOperationManualOfMyMicrowaveOven {English, Spanish}

However, within frameworks that the observer fails to constrain into bi-modal perception, it is impossible to express mutual individual antonyms

• myTemplate{red, orange, yellow, green, blue, purple}
• colour{continuous spectrum}

Where you could only say

• The opposite of red template = not red = the set of all other colours in myTemplate besides red
• The opposite of green colour = not green = infinite collection of all colours except those regions perceived as green

One could also derive the pleasure from having antonyms, by defining an ordered set.

For example, let's define that enumeration order proceeds from left to right in the following frameworks

• temperatureSetting{hot, medium, cold}
• computerGameOfClones{love, friend, hate}

In such settings, it would not be difficult to surmise what you would be asking

• what is the opposite of hot temperature setting
• what is the opposite of love relationship

because they are in an ordered set, where the opposite of one extremity is the other extremity within a one dimensional vector. You are merely implicitly defining a bi-modal (i.e., two valued) set of extremities from a range of labels.

It is also not difficult to surmise

• what is opposite of medium in my air-cond setting
  where answer is the set of extremities{hot, cold}
• what is opposite of friend in GameOfClones
  where answer is the set of extremities{love, hate}

OTOH, let's consider a multidimensional framework

AirCondSetting{
  power{on, standby, scheduled, off} , 
  temperature{hot, medium, cold} ,
  mode{summer, springfall, winter, userprg1, userprg2, userprg3}
}

And then let's ask the unanswerable questions

• What is the opposite of userprg3?
• What is the opposite of mode?

Further, let's consider a multiple membership entity where shoes could be a member in any of the the following sets.

• set of apparel {shirts, trousers, scarves, shoes, blouses, ... etc}
• set of footwear {slippers, socks, stockings, shoes, sole pads, ... etc}
• set of impediments to rescuing from car accidents {jackets, boots, shoes, wristwatches, belts, ... etc}

Then, you wish to ask the question

What is the opposite of shoes?

There isn't an answer because

1. You did not specify which association of membership in which shoes are found: set of apparel, set of footwear, set of impediment, set of ego statements ...
2. You did not constrain any of the possible sets into perceivable bi-modal abstracts, implicitly or explicitly.

Therefore, when you ask

What is the antonym of stage name?

1. You did not specify the association membership: stage, public persona, online avatar, legal, etc.
2. You did not present any constrains that might help to arrange these associations into an ordered set, to see if we could find stage name as one of the extremities.

If by "stage name" you mean "a name artists use at work", the opposite of that is "real name", the official name they're registered as to the government

Of the three options that are offered within the body of the question as possible answers, given name is definitely not the right one, as it usually used in contrast to surname (or family name), and what is sought seems to be a term for something that includes a surname. Birth name and real name can both be used in contrast to stage name, but they don't always stand for the same thing, as one may change one's birth name to another name, which one then proceeds to use for all purposes that are not related to one's acting career, and have yet another name as one's stage name. Most commonly, that's the case when a woman adopts her husband's surname; if one asks of such a woman 'I know what her stage name is, but what's her real name?', the correct answer would be the name she currently uses outside the theatre world, not the birth name.

Most of the above has already been noted in a comment by BoldBen. What needs to be clarified is that real name does not have a precise context-independent meaning, because it is always used in contrast to some other kind of a name, and its use requires a context that makes it clear what the relevant other kind of a name is. Sometimes, the other name is the stage name of an actor, but it can also be a nom de plume of a writer, a username of a subscriber to an online service, an alias of spy, or of a criminal, a code name used for secrecy, or simply a nickname. The question 'What's his real name?' may thus have different answers in different contexts. For example, if it asked of an actor 'I know what his stage name is, but what's his real name?', the answer may be 'John Smith', if that's the name by which he always introduces himself outside the theatre world, but, in a different context, we may say of the same person that his real name is 'Johannes Smith', if that's what appears in his passport.

Thus, even though real name is probably the best term for the OP's purposes, it may not always be precise enough for the purposes in which a lot depends on the answer. In such cases one may need a longer phrase that specifies fully what kind of a name is needed, such as your name, as it appears in your current passport or the name under which you graduated from this university.