Here's an epistemological head-scratcher: do the odds still change if you don't hear the daughter's name accurately? Why?

Remember, those odds are the level of certainty you have that a given statement may be true based only on what you already know. You can also assign a level of certainty to the facts you think you know.

Given the number of ways to mishear "Mary" and the dialectical variant in pronunciation characterized by the Mary-marry-merry merger, I'd tentatively assign the following values:

  25% One child is a girl.  (Heard correctly)
  25% One child is a boy.   (Heard incorrectly)
  50% No new information.   (Incomprehensible or ambiguous)

  In the first case P(A and B|A) = P(A and B|B) = 1/2
  In the second, P(A and B|!A) = P(A and B|!B) = 0
  In the third, P(A and B|A or B) = 1/3

In any case, you're just guessing at the probability you might mishear something, so there's no definitive answer. The mere possibility that I might have heard a boy's name means that the overall probability could be anywhere between 0 and 1/2. By the above, my new odds are 5/12.

So the odds do change, based on your confidence in what you heard (and your confidence that your friend isn't the kind of parent to name her son "Meriadoc" or something similar).