A problem with Quirrell's heroic alter ego being Tom Riddle, even if the only ones who know Tom Riddle is Voldemort are the inner circle of the Order of the Phoenix, is, why wouldn't madam Bones tell Dumbledore that Tom Riddle is currently inhabiting Quirrell's body?

Quirrell said that he "reported to the headmaster" by which I interpret Dumbledore wants to know in what ways the defense professor was involved in this whole debacle, from which we can infer that he will have or has had Bones report to him as well. The fact that a war hero that was an incredibly powerful wizard as well and led forces against death eaters in various occasions is inhabiting the body of your defense proffesor is not trivial. And then Quirrell also outright TELLS Bones that Dumbledore doesn't know his identity, so we can be sure that Amelia will be reporting that this alleged hero, whatever his identity is, is currently posing as professor Quirrell.

I had assumed before that Dumbledore knew Quirrell's identity, that perhaps he was told that upon his travels after his graduation, Quirinus Quirrell had stumbled upon an ancient tomb containing the soul of a powerful and clever dark wizard, and this spirit had taken possession of Quirrell's body. Dumbledore, accepting this, agrees to let him teach at Hogwarts given that he will be able to teach things to his students few other wizards will be able to. Or something along those lines.

But not before a warning the staff about his nature and making sure things don't get too freaky. From chapter 15:

"Now repeat after me," said Professor McGonagall. (...)

"Even if the current Defense Professor at Hogwarts tells me that a Transfiguration is safe, and even if I see the Defense Professor do it and nothing bad seems to happen, I will not try it myself."

After all, they've had all sorts of wacko defense professors already. From chapter 70:

"My goodness," said Penelope Clearwater. "I think that's the most overtly evil Defense Professor we've ever had."

Professor McGonagall coughed warningly, and the Head Boy said, "You weren't around for Professor Barney," which made several people twitch.

So it's just another year at defense class.

But now it turns out Dumbledore doesn't know his identity? Or does he actually know it and it turns this fabricated heroic identity is not Tom Riddle? If he actually doesn't know, what is he playing at, hiring some incredibly powerful wizard from Merlin knows where who is obviously untrustworthy and likes to plot an awful lot? Dumbledore at one point states the three most powerful wizards in the school are him, Snape, and Professor Quirrell.

And the worst thing is that it actually does fit if the slytherin hero who rose against the death eaters and disappeared suddenly happened to be Riddle.

-Born in 1926

-Sorted into Slytherin

-People speaking of him as the next Dumbledore

-Likes to wander off in Albania

-Of noble house descent

I'm assuming that given how the politics and nobility work in MoR, House Gaunt didn't lose all their gold, or at least not in the same fashion as in canon given that there is probably some sort of convenient system to prevent this. But then again, House Potter did just go broke. And we are told that his grandmother is the Lady of his House. We do never see Merope's mother in canon; so I'm assuming that if the differences from canon are enough to keep House Gaunt from poverty, perhaps it's not all that strange if her mother is alive as well. However, it was Riddle's grandfather, not grandmather, who bore the name of Gaunt. If he died, would her wife inherit his title? I'm thinking not. Or perhaps yes if she was of noble ancestry herself, which is a given considering we are talking about someone who married a Gaunt. And if this new heroic figure wasn't Tom Riddle, then can we assume it was an actual heroic person and Voldemort it taking advantage of his story to cover his usage of Quirrell's body? After all, they were born in the same year, and I can't imagine Riddle manipulating another person since he was eleven years old into being Voldemort's nemesis for a huge social experiment in years to come. Or could he?

I notice I am terribly confused.

And Quirrell does speak about playing the two sides in different occasions, and he did sound to me like he was talking about a social experiment when talking to Hermione, on which he was a leader in both sides of the conflict, and whose outcome he did not expect:

Professor Quirrell shook his head as though in bemusement. "And it was the strangest thing - the Dark Wizard, that man's dread nemesis - why, those who served him leapt eagerly to their tasks. The Dark Wizard grew crueler toward his followers, and they followed him all the more. Men fought for the chance to serve him, even as those whose lives depended on that other man made free to render his life difficult... I could not understand it, Miss Granger."