Why do some POV characters have titles, not names, for chapters?

Question

Starting from A Feast for Crows, certain characters get titles like "The Prophet" (Aeron), "The Soiled Knight" (Arys) and "The Captain of the Guards" (Areo). I'm still not sure why.

AWOIAF tries to explain it on its page about POV characters...

Minor POV characters: Introduced in "A Feast for Crows", this category includes POV chapters from 'minor' characters rather than the major protagonists of the series. They are differentiated from the main POVs by having a descriptive title rather than just a name.

...but then renders this explanation unsatisfactory with the following:

As the books progress however, the distinction between major and minor characters is blurred; some less frequent POVs such as Melisandre, and starting in A Dance with Dragons, Victarion, have their names as chapter titles, whereas some more frequent POVs such as Arya and Theon are given descriptive titles.

So, I'd like to know if GRRM has addressed any of these questions:

1. Why did he choose to do this at all? What did it add to the story?

2. Why is the process so arbitrary, with some characters referred by titles and some not? As AWOIAF points out, it cannot relate to the importance of the character, because Arya (as one of the most major characters) is given a title for a chapter name, and Melisandre (who has one chapter,) isn't.

3. Why do the characters' titles change every time they get a new chapter?

Answer 1

Good question. According to this report from Boskone in Feb 2013, there is a reason but GRRM will not reveal it, at least for now:

I asked whether he would comment on his choice to call these chapters “Ser Barristan” instead of continuing with the titles from ADWD, and he replied that he has “a method to his madness” for promoting characters with descriptors to named characters but that he didn’t want to say more.

For what it's worth, here is a list of all the chapter titles without names:

The Prophet, The Captain Of Guards, The Kraken's Daughter, The Soiled Knight, The Iron Captain, The Drowned Man, The Queenmaker, Alayne I, The Reaver, Cat Of The Canals, The Princess In The Tower, Alayne II, The Merchant's Man, Reek I, Reek II, The Lost Lord, The Windblown, The Wayward Bride, Reek III, The Prince of Winterfell, The Watcher, The Turncloak, The King's Prize, The Blind Girl, A Ghost in Winterfell, The Queensguard, The Iron Suitor, The Discarded Knight, The Spurned Suitor, The Griffin Reborn, The Sacrifice, The Ugly Little Girl, The Kingbreaker, The Dragontamer, The Queen's Hand

As to the reason for GRRM's reasoning:

Some have speculated that perhaps the players in the game of thrones are given named titles, whereas "pieces" in the game (IE, minor characters) are given descriptive titles.

Answer 2

It's a nod to how the characters are thinking and behaving for themselves. So it would seem that the titles are descriptive for what happens to that character during the chapter.

Likewise, he mentioned that the titles of the chapters in AFfC were a nod to how the characters think of themselves - most especially Sansa. He wants to get back to writing ADwD, but so far touring has severely curtailed his productivity.
_{So Spake Martin, Boskone (Boston, MA; February 17-19)}

This is also alluded to in the following comment be George R. R. Martin.

The audience member then asked about the changing atmosphere in the books, and George said that yes, it changes with the action in the books, and the changing situations of characters.
_{So Spake Martin, Stockholm and Archipelacon Report}