I was re-reading GoF and I realized how Dumbledore never calls Harry "Mr. Potter", though he almost always calls the other students "Mr. Longbottom" or "Mrs. Granger". Or, if he does use their first names, he still calls them "Mr. Neville Longbottom". For Harry he might say "Mr. Harry Potter", but he never says "Mr. Potter". I might have not seen a place where he called him simply by his last name, but I don't think so. Here is my little theory on why that is so in a monologue by Dumbledore.
A/N after being written: This turned into a lot more than the above summary.
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Albus Dumbledore sighed as he walked away from the infirmary after leaving young Harry Potter under the capable hands of Madame Pomfery, Mrs. Weasley, and the strongest sleeping potion that Severus Snape could brew.
Harry Potter, he thought, famous before he could remember, growing up in a home where he was neglected and abused, and now realizing what his birthright meant. He was a carbon copy of his father in every way; all except for his eyes, those were his mothers...
James and Lily Potter, they had been friends before they fell in love. Everyone knew they would end up together, he remembered that a few of the teachers had even had a betting pool going whether or not they would end up together. He frowned slightly, another subject in the teachers betting was if Peter Pettigrew would ever be successful on his own, well, he had come to more success in his endeavors then anyone had thought he would. The truth of those exploits, were not known and left an innocent man to suffer.
So now Voldermort had come back to power. He had seen the signs and with help from the centaur's star reading skills and Sybil Trewlaney's trance-like prediction last year he had quietly begun preparing for what would follow. Harry Potters blood protection from the Durseleys had been reinforced and he had begun gathering the old crowd together. He had hired Alastor Moody because he could provide extra protection for the school as well as teaching DADA better than almost anyone else could. That plan had backfired…Moody, his old school friend stuck inside of a trunk for the entire school year right below his nose! Well, he smiled with black humor, this certainly wouldn't help his paranoia! Now what had been a prediction was a reality, he sighed as he walked into his office.
Unlike the other students he had never called Harry solely by his last name, that was what he had called James, and out of respect he called Harry by his entire or first name. What had happened on Halloween in Godric's Hollow had been partly his fault, had he been adamant about being the Potters secret keeper himself Harry would not be an orphan.
Yes, but than Voldermort would never have been stopped and you would probably be dead along with almost everyone else that you know, he voice of reason inside his head said. Harry's parents died to save everyone, their sacrifice had been more than most could fathom.
A nagging voice still proclaimed that it was his fault but he silenced it, turning his mind to other thoughts. That Harry had inherited his father's bravery was definite. He had a sudden vision of himself standing behind his desk scolding James Potter for being in the Forbidden Forest, well scolding, but than afterwards winking and sending him an invisibility cloak. He had sent the invisibility cloak anonymously, but James Potter had always known.
"The Marauders," he thought and smiled, James, Lupin, Sirius…and on the outskirts, Peter. Than, there were their female counterparts, all dead now from Voldermort. The Marauders had all been engaged or had a serious girlfriend at one point except for Peter. He remembered the girls simply falling over Sirius with his dark hair, and eyes, and a spark of romance that had even the most serious among them giggling wildly. He'd last been with that Ravenclaw girl named Rebecca, she killed herself immediately after Sirius was sent to Azkaban, leaving behind a note explaining that
"Everyone else is dead, I am dead already in soul and I now join them in body".
He shuddered remembering how she'd drunken the potion to end her life, she'd always been particularly good in potions for a non-Slytherin, and fantastic in every class with the typical Ravenclaw brains. He wondered if she had known that Sirius was innocent. James Potter, Sirius Black, and Remus Lupin, a tighter group of friends had never been before, you never saw one without the others, not even when Remus was transforming, yes, he knew of those nights as well. He knew he should have stopped them from this, but he believed in their abilities and they provided a family for Remus Lupin, something he'd never had much of. His own father had bitten him in a transformation accidentally, causing him to commit suicide a few years later.
Harry and James Potter, so alike in all ways they could have been twins born years apart. Every time the professor saw him he almost believed that his former student had become a ghost. No wonder Severus was so cruel to the boy; he was identical to the man who he hated so much. He knew that he would never be able to call Harry "Mr. Potter", that name belonged to one who had never been able to pass it on to his child, out of respect for the dead that name would not be used for this child
.Respect for a student, respect for a friend, respect for a powerful wizard, respect for a father who gave the ultimate sacrifice, respect for the dead.
The door to Albus Dumbledore's study closed as he began planning for what the future would bring.