I will start my answer by first scrutinizing how embedded questions are formed:
- When will the match start?
This is an interrogative sentence. The answer is, say, at x. x can be anything, any time.
So the answer to this question is:
- The match will start at x.
Now see how in interrogative sentence when fills the gap:
- The match will start ____
- The match will start when
Now in question the interrogative word - when is fronted, and subject-auxiliary is inverted -
- When will the match start?
Let's now form the embedded question:
- I don't know x.
- I don't know the match will start ____
- I don't know the match will start when.
- I don't know when the match will start.
Now let's focus on a similar sentence as the one OP quoted:
- (i) I don't know X
- (ii) X is your name. (Question: What is your name?) [Notice no subject-auxiliary in version in question]
- (iii) Your name is X (Question: What is your name?) [Notice here the subject-auxiliary inversion took place]
Both (ii) and (iii) basically mean the same thing, but structurally they are different. In (ii) X is the subject, but in (iii) X is in predicative complement.
Now we will form the embedded question based on sentence (ii)
- I don't know ___ is your name.
- I don't know what is your name.
Now we will form the embedded question based on sentence (iii)
- I don't know your name is ___.
- I don't know your name is what.
- I don't know what your name is.
So in OP's original sentence both the sentences are correct, and mean the same thing.
[N.B - Based on various corpus and google book search, I think Let's see who the real man is. is more common]