The only information Tom Marvolo Riddle has about his parents are in his name.
In HP 6 Dumbledore shows Harry how Voldemort found the house of the Gaunts before learning about his father, who might have been easier to find, given that he knew his whole name.
So how did he find out about the Gaunts and how did he find their house?
Voldemort had a number of clues to work with, notably an attack that was recorded by the Ministry of Magic and which resulted in a charge being filed. Assuming wizarding justice is anything like muggle justice, both the name of the accused (Marvolo) and his victim (Tom Riddle) would be a matter of public record.
‘Oh, she survived,’ said Dumbledore, reseating himself behind his desk and indicating that Harry should sit down too. ‘Ogden Apparated back to the Ministry and returned with reinforcements within fifteen minutes. Morfin and his father attempted to fight, but both were overpowered, removed from the cottage and subsequently convicted by the Wizengamot. Morfin, who already had a record of Muggle attacks, was sentenced to three years in Azkaban. Marvolo, who had injured several Ministry employees in addition to Ogden, received six months.’ ‘Marvolo?’ Harry repeated wonderingly.
‘That’s right,’ said Dumbledore, smiling in approval. ‘I am glad to see you’re keeping up.’
‘That old man was –?’
‘Voldemort’s grandfather, yes,’ said Dumbledore. ‘Marvolo, his son Morfin and his daughter Merope were the last of the Gaunts, a very ancient wizarding family noted for a vein of instability and violence that flourished through the generations due to their habit of marrying their own cousins. Lack of sense coupled with a great liking for grandeur meant that the family gold was squandered several generations before Marvolo was born. He, as you saw, was left in squalor and poverty, with a very nasty temper, a fantastic amount of arrogance and pride, and a couple of family heirlooms that he treasured just as much as his son, and rather more than his daughter.’
‘So Merope,’ said Harry, leaning forwards in his chair and staring at Dumbledore, ‘so Merope was … sir, does that mean she was … Voldemort’s mother?’
‘It does,’ said Dumbledore. ‘And it so happens that we also had a glimpse of Voldemort’s father. I wonder whether you noticed?’
‘The Muggle Morfin attacked? The man on the horse?’
‘Very good indeed,’ said Dumbledore, beaming. ‘Yes, that was Tom Riddle Senior, the handsome Muggle who used to go riding past the Gaunt cottage and for whom Merope Gaunt cherished a secret, burning passion.’
This is what Dumbledore has to say about the question:
All he had to go upon was the single name “Marvolo”, which he knew from those who ran the orphanage had been his mother’s father’s name. Finally, after painstaking research through old books of wizarding families, he discovered the existence of Slytherin’s surviving line. In the summer of his sixteenth year, he left the orphanage to which he returned annually and set off to find his Gaunt relatives.
(Harry Potter and the Half-Blood Prince, chapter A sluggish memory)
He did not find his father because he had assumed him to be a wizard and therefore searched in the wrong places. Dumbledore again:
It seems that he searched in vain for some trace of Tom Riddle Senior on the shields in the trophy room, on the lists of prefects in the old school records, even in the books of wizarding history. Finally he was forced to accept that his father had never set foot in Hogwarts. I believe it was then that he dropped the name for ever, assumed the identity of Lord Voldemort, and began his investigations into his previously despised mother’s family – the woman whom, you will remember, he had thought could not be a witch if she had succumbed to the shameful human weakness of death.
