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In Guards! Guards! Sam Vimes is surprised that Ankh-Morpork used to have a king:

Vimes shook his head. The world was definitely going mad around him. "You've lost me there," he said.

"Air," said Throat patiently. "You know. Air to the throne."

"What throne?"

"The throne of Ankh."

"What throne of Ankh?"

"You know. Kings and that." Throat looked reflective. "Wish I knew what his bloody name is," he said. "I put an order in to Igneous the Troll's all-night wholesale pottery for three gross of coronation mugs and it's going to be a right pain, painting all the names in afterwards. Shall I put you down for a couple, Cap'n? To you ninety pence, and that's cutting me own throat."

Vimes gave up, and shoved his way back through the throng using Carrot as a lighthouse. The lance-constable loomed over the crowd, and the rest of the rank had anchored themselves to him.

"It's all gone mad," he shouted. "What's going on, Carrot?"

"There's a lad on a horse in the middle of the plaza," said Carrot. "He's got a glittery sword, you know. Doesn't seem to be doing much at the moment, though."

Vimes fought his way into the lee of Lady Ramkin.

"Kings," he panted. "Of Ankh. And Thrones. Are there?"

"What? Oh, yes. There used to be," said Lady Ramkin. "Hundreds of years ago. Why?"

"Some kid says he's heir to the throne!"

However in later books he knows about his ancestor "Old Stoneface" Vimes who beheaded the last king. When and how does Sam learn about him?

Suffer-Not-Injustice Vimes' existence was apparently common knowledge in Ankh Morpork education, at least according to Dragon King of Arms.

“Indeed. Ah-ha. Suffer-Not-Injustice Vimes. Your ancestor. Old
Stoneface, indeed, as he was called. Commander of the City Watch in
1688. And a regicide. He murdered the last king of Ankh-Morpork, as every schoolboy knows.”

_{^{Terry Pratchett: Feet of Clay}}

This would strongly suggest that Samuel Vimes' ignorance (in 'Guards, Guards') of both the existence of a Kingdom of Ankh Morpork and his own ancestor's part in King Lorenzo's downfall is probably best attributed to his own poor schooling, or possibly the fact that Dragon's knowledge of contemporary education is woefully out of date.

We can safely presume that the events of Guards, Guards and the persistent rumours of an extant King were sufficient to get adult Sam Vimes to show a greater interest in Ankh Morpork's history whereupon he discovered that his distant relative was 'Old Stoneface'.

We do know that at some point, Sam Vimes read about him in various history books.

“He, er, doesn’t appear much in the history books,” said Vimes.
“Sometimes there has to be a civil war, and sometimes, afterwards,
it’s best to pretend something didn’t happen. Sometimes people have to
do a job, and then they have to be forgotten. He wielded the axe, you
know. No one else’d do it. It was a king’s neck, after all. Kings
are,” he spat the word, “special. Even after they’d seen the…private
rooms, and cleaned up the…bits. Even then. No one’d clean up the
world. But he took the axe and cursed them all and did it.”

...

“I didn’t know this,” he said. “I thought there was just some wicked rebellion or something.”

Vimes shrugged. “It’s in the history books, if you know where to
look.”

_{^{Terry Pratchett: Men At Arms}}

We know that as an adult he went to the University Library and read his ancestor's journal.

Suffer-Not-Injustice Vimes wasn’t a pillar of the community. He killed
a king with his own hands. It needed doing but the community, whatever
that was, didn’t always like the people who did what needed to be done
or said what had to be said. He put some other people to death as
well, that was true, but the city had been lousy, there’d been a lot
of stupid wars. We were practically part of the Klatchian empire.
Sometimes you needed a bastard. History had wanted surgery. Sometimes
Dr. Chopper is the only surgeon to hand. There’s something final about
an axe. But kill one wretched king and everyone calls you a regicide.
It wasn’t as if it was a habit or anything…

Vimes had found Old Stoneface’s journal in the Unseen University
library. The man had been hard no doubt about that. But they were hard
times. He’d written: “In the Fyres of Struggle let us bake New Men,
who Will Notte heed the Old Lies.” But the old lies had won in the
end.

_{^{Terry Pratchett: Feet of Clay}}

His trial was apparently quite famous, as were his last words.

Mrs Proust hesitated for a moment, and then said, ‘Well, if it’s true
about what they found in his private dungeon, then the answer is “yes”
in great big letters. They put the commander’s ancestor on trial
anyway, because chopping heads off kings always causes a certain
amount of comment, apparently. When the man stood in the dock, all he
said was, “Had the beast a hundred heads I would not have rested until
I had slain every last one.” Which was taken as a guilty plea. He was
hanged, and then much later they put up a statue to him, which tells
you more about people than you might wish to know. His nickname was
Old Stoneface, and as you can see, it runs in the family.’

_{^{Terry Pratchett: I Shall Wear Midnight}}

The real answer is that at this point in the story Sam Vimes was not yet the character he would later become and in a series as complex as the Discworld you have to cut the author a bit of slack to retcon things a bit.

There are also some solid in-world excuses. Firstly during the events of Guards Guards Sam Vimes was a semi-functional alcoholic who has more or less given up on his principals so it is not unreasonable that he is not entirely up to speed on even his own knowledge of events.

We also have a few points when he has specific reason to get reacquainted with his family history the first is is in Men at Arms when he both encounters Ankh-Morpork's College of Arms and marries into the nobility.

Secondly in Jingo he specifically researches heraldry and the Ankh-Morpork constitution (following a hint from Lord Vetinari) to discover that as a knight he has the right to raise a regiment of his own in time of war.

It is also reasonable to suppose that his wife, as one of the oldest aristocratic families in the city would have been aware of the history of his name.

It is also possible to assume that given his poor background (as explained in Night Watch) he could never be that sure of his heritage, but just latched onto Stoneface Vimes because of the common surname and because he could relate to him. We can further speculate that Lord Vetinari recognised something in Vimes's character which was useful and encouraged or even planted the seeds of this association.

There is also the time patching and jumbled history established in Thief of Time and the fact that Vimes is established as a significant historical figure who gets involved in a time paradox in Night Watch not to mention the fact that he has been an avatar of a demon of vengeance in Thud and the idea that the Discworld is a bit odd and responds to magic and narrative causality has been established from the very first book.

So in a very real sense Sam Vimes is the hero that the Discworld NEEDS.

There are no inconsistencies in the Discworld books; ocassionally, however, there are alternate pasts.

Terry Pratchett

The out-of-universe-answer is that at the time he obviously didn't have the whole background of the character filled out. Indeed Early Installment Weirdness.

It would also be conceivable that as Stoneface was known at the time only as a murderer of kings, Sam Vimes may not have wanted to investigate the connection until marriage & nobility forced him to.