A Very Brady Confusion

Cynthia Brady. Marsha Brady. Jan Brady.

...
Ok, I came home from work. There was nothing on TV, so I left it on one of those holiday specials on TBS. Then, at 7pm, A Very Brady Christmas came on. I did not watch it the movie, but I did manage to make it through the intro. Then, a thought occurred to me. I have never thought about this before.
Why is the girls' last name "Brady"?

Perhaps they explain this in the movies? I cannot remember much about them.

However...it seems to me that the girls' last name SHOULD be the last name of their father. Now, I will admit, it is possible that their father's name was also Brady, but it is highly unlikely.
I just do not understand that.

I know that was random. Oh well. I just figured I would post about it before I forgot I was confused.