In Judges 13, a very important interchange between two individuals occurs.  Interestingly, we are not provided with the names of either one.  One is a woman, referred to as Manoah's wife, and the other is referred to as "The angel of the Lord".  The angel appears to Manoah's wife, up to that time "barren and childless", and tells her that she is going to become pregnant and give birth to a son.

"Now see to it that you drink no wine or other fermented drink and that you do not eat anything unclean.  You will become pregnant and have a son whose head is never to be touched by a razor because the boy is to be a Nazirite, dedicated to God from the womb.  He will the lead in delivering Israel from the hands of the Philistines."

She tells her husband about the visitation and instructions, and Manoah prays to the Lord for the "man" to appear again and provide instructions.  Interestingly, in answer, the angel does appear again, but once again it's to Manoah's wife, and she has to go get Manoah.  The angel waits and when Manoah asks him for instructions, the angel begins with "Your wife must do all that I have told her.", repeats his instructions, and says "She must do everything I have commanded her.".  In other words, the visitation to Manoah's wife should have been regarded as sufficient.

Manoah proceeds to ask the angel his name and gets the reply "Why do you ask my name?  It is beyond understanding."  (Very interesting, right?  One translation*:  "You wouldn't understand -").  Manoah asks the angel to accept a meal, but the angel suggests that Manoah make an offering to the Lord.  When Manoah offers a sacrifice, the angle jumps into the fire and ascends to Heaven, scaring the daylights out of Manoah.  "We are doomed to die!", he said to his wife.  "We have seen God!".  But his wife answered, "If the Lord had meant to kill us, he would not have accepted a burnt offering and grain offering from our hands nor shown us all these things or told us this". 

So an unnamed angel visits an unnamed woman and entrusts her to an extremely important job.  The woman then has to use logic to calm down her named, panicking husband (to whom the angel did not choose to appear directly to). 

The business of God does not have to conform to human convention, whether in a male-dominated society or otherwise.  If the Lord understands that the reliable, calm, intelligent person is a woman instead of a man, that's completely His business.  If the name of the angel and the name of the woman are not revealed, it doesn't detract from the extreme importance of the event and its results.

Most Biblical text used here is from the New International Version

*The Message version:  "You wouldn't understand -"

(Good News version:  "... It is a name of wonder.")