Maybe the 4th wanted Naruto to use his mother's name because she died giving birth to him, or died shortly after his birth or something. Seems like something a father would do. Would also take care of the 'you want to do what?!' response he would get asking her to let him 'seal the demon fox in our son'. Though likely since he was hokage there would be little objection anyways.

Would be nice if we found out more in the Jiraiya Special, though I'm not counting on it.