Barenaked Ladies

I have followed and enjoyed the music group the "Barenaked Ladies" from it's earliest days. Many have considered the origins of the naming and so have I. Four guys gathering to create their persona. A name needs to attract their target market. What do guys consider a must-see. Seen in this light "Barenaked Ladies" is logical.
...but I ponder:
"Would a lady be barenaked?"
Am I a prude?
...using the same reasoning as the guys employed:
"What would a group of woman call their music group?"
Men doing housework...?
Is that an original thought?