Why did the name 'Riddle' ring a bell to Harry?

Question

When Ron and Harry find the diary, a name is written on it : "T. M. Riddle". If I'm not mistaken, the quote below is the first time we hear about the name Riddle:

Harry saw at once that it was a diary, and the faded year on the cover told him it was fifty years old. He opened it eagerly. On the first page he could just make out the name “T. M. Riddle” in smudged ink.
(Chamber of Secrets, Chapter 13, The very secret diary)

Ron knows the name because he polished Riddle's shield many times during detention, but otherwise they don't seem to know it.

“I know that name... T. M. Riddle got an award for special services to the school fifty years ago.”
“How on earth d’you know that?” said Harry in amazement.
“Because Filch made me polish his shield about fifty times in detention” said Ron resentfully.
(Chamber of Secrets, Chapter 13, The very secret diary)

Yet the name rings a bell to Harry... why?

And while Harry was sure he had never heard the name T. M. Riddle before, it still seemed to mean something to him, almost as though Riddle was a friend he'd had when he was very small, and had half forgotten. But this was absurd. He'd never had friends before Hogwarts, Dudley had made sure of that.
(Chamber of Secrets, Chapter 13, The very secret diary)

Answer 1

Probably because of his connection with Voldemort

It is true, Harry never seems to have seen (or at least is not mentioned as having seen) Riddle's name before he sees the diary.

However, he does have a supernatural connection to Riddle:

“You can speak Parseltongue, Harry,” said Dumbledore calmly, “because Lord Voldemort — who is the last remaining descendant of Salazar Slytherin — can speak Parseltongue. Unless I’m much mistaken, he transferred some of his own powers to you the night he gave you that scar. Not something he intended to do, I’m sure. . . .”

“Voldemort put a bit of himself in me?” Harry said, thunderstruck.

—Harry Potter and the Chamber of Secrets

As we later find out,

this is because Harry is a Horcrux.

It is this, I think, that causes him to recognize Riddle's name: he has something of Voldemort within him.

Answer 2

As a Horcrux, the diary affected those nearby. It was already working its magic on Harry.

For me, this has less to do with the piece of soul in Harry and more to do with the piece of soul in the diary. We know from Deathly Hallows that getting close to a Horcrux can result in the soul fragment affecting someone's mood or behaviour. Ron is more argumentative and sensitive when he's wearing the locket. This hints at one of Voldemort's key skills: creating division.

Here he is exercising another one of his skills: charm. Realistically, a blank diary is of no use or interest to Harry so he should throw it away. Yet to unleash the Basilisk and reopen the Chamber of Secrets Riddle needed Harry/Ginny to not only keep it but allow it influence over them. So as soon as they wrote in it Riddle wrote back, using his natural talent for manipulation to win them over.

"It's very boring, having to listen to the silly little troubles of an eleven-year-old girl," he went on. "But I was patient. I wrote back, I was sympathetic, I was kind. Ginny simply loved me. No-one's ever understood me like you, Tom...I'm so glad I've got this diary to confide in...It's like having a friend I can carry round in my pocket..."
Riddle laughed, a high, cold laugh that didn't suit him. It made the hairs stand up on the back of Harry's neck.
"If I say it myself, Harry, I've always been able to charm the people I needed. So Ginny poured out her soul to me, and her soul happened to be exactly what I wanted."
_{(Chamber of Secrets, Chapter 17, The Heir of Slytherin)}

Yet even before Riddle was able to influence them directly through his writing the Horcrux was having an almost magnetic pull on those who emotionally attached themselves to it or who put themselves in close proximity to it. Harry is naturally inquisitive and so was perhaps more naturally drawn to the diary than someone else might be. Nevertheless, the way in which Harry seemed to think of Riddle as a friend even at this early stage is, for my money, down to the power of the Horcrux.