Which is his name: the Fat Friar, Fat Friar?

Question

Then something happened that made him jump about a foot in the air - several people behind him screamed.
"What the ––?"
He gasped. So did the people around him. About twenty ghosts had just streamed through the back wall. Pearly-white and slightly transparent, they glided across the room talking to one another and hardly glancing at the first years. They seemed to be arguing. What looked like a fat little monk was saying: "Forgive and forget, I say, we ought to give him a second chance ––"
"My dear (i) Friar, haven't we given Peeves all the chances he deserves? He gives us all a bad name and you know, he's not really even a ghost –– I say, what are you all doing here?"
A ghost wearing a ruff and tights had suddenly noticed the first years. Nobody answered.
"New students!" said (ii) the Fat Friar, smiling around at them. "About to be Sorted, I suppose?"
A few people nodded mutely.
"Hope to see you in Hufflepuff!" said (iii) the Friar. "My old house, you know."
"Move along now," said a sharp voice. "The Sorting Ceremony's about to start."
(J. K. Rowling, Harry Potter and the Sorcerer's Stone)

What is the ghost’s name: Fat Friar, the Fat Friar, or other something? The first thing that arose in my mind is his is ‘the Fat Friar’, just as these names: the United Kingdom, the Philippines, which give referentiality/defiteness on united kingdom and Philippines. But there being three types of calling, I’m not sure if my guessing is proper.

Answer 1

None of these is a name.

Friar, if lowercased, designates a man who has taken religious vows and joined a mendicant order. Uppercased it is the title by which a friar is referred to and addressed, like ‘General’ or ‘Doctor’.

If the friar's religious name were ‘John’, he would be referred to as ‘Friar John’; but since it appears that no one at Hogwarts knows this friar's name, he is referred to either as ‘the Friar’ or by the sobriquet or nickname ‘the Fat Friar’.^† The determiner shows that this is not an actual name and the capitalization shows that it is proper to a specific individual.

If his name were known he might be addressed as ‘Friar John’. Since it is not known, and since it would be rude to address him as ‘Fat Friar’, he is addressed simply as ‘Friar’, just as you might address a military man as ‘General’, or your teacher as ‘Professor’.

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^† This appears to be the usual reference among Hogwarts students: “The Fat Friar told me — that Umbridge tried to get back into his office last night after they'd searched the castle and grounds for him.” —Harry Potter and the Order of the Phoenix