Why do young witches & wizards know Voldemort's name?

Question

1. There is a taboo against speaking 'Voldemort' at the beginning of Book One (not the Taboo placed by the Ministry in Book Seven).
2. Every student Harry meets gasps at Harry's audacity in saying 'Voldemort' instead of You-know-who.
3. Point 2 means somebody told them the name, most likely their parents.
4. Point 3 means there is no taboo.

Is it because logic is a branch of mathematics, and maths and JKRmagic don't mix well?

If wizarding parents were so afraid of Voldemort's memory to avoid mentioning him by name, why would they tell the name to their kids and then forbid them from using it? Makes as much sense as parents forcing children to learn the whole obscene vocabulary at the age of six, and then telling them not to use swearwords.

Answer 1

First, the Taboo (as opposed to a taboo) did not exist until Book 7

“Sorry.” said Ron, wrenching Harry back out of the brambles, “but the name’s been jinxed. Harry, that’s how they track people! Using his name breaks protective enchantments, it causes some kind of magical disturbance—it’s how they found us in Tottenham Court Road!”

We see that the name has been jinxed; this is a new development. The opposite would not make any sense: why would the pre-Voldemort Ministry be interested in catching people who said Voldemort's name? Voldemort, on the other hand, knows that only those who stand up to him use his name as a matter of course:

"You’ve got to give them credit, it makes sense. It was only people who were serious about standing up to him like Dumbledore, who ever dared use it. Now they’ve put a Taboo on it, anyone who says it is trackable—quick-and-easy way to find Order members!"

We also see that Hagrid is willing to say the name if necessary

He sat down, stared into the fire for a few seconds, and then said, "It begins, I suppose, with -- with a person called -- but it's incredible yeh don't know his name, everyone in our world knows --"

"Who? "

"Well -- I don' like sayin' the name if I can help it. No one does."

"Why not?" "Gulpin' gargoyles, Harry, people are still scared. Blimey, this is difficult. See, there was this wizard who went... bad. As bad as you could go. Worse. Worse than worse. His name was..."

Hagrid gulped, but no words came out.

"Could you write it down?" Harry suggested.

"Nah -can't spell it. All right -- Voldemort. " Hagrid shuddered. "Don' make me say it again. Anyway, this -- this wizard, about twenty years ago now, started lookin' fer followers. Got 'em, too -- some were afraid, some just wanted a bit o' his power, 'cause he was gettin' himself power, all right. Dark days, Harry. Didn't know who ter trust, didn't dare get friendly with strange wizards or witches... terrible things happened. He was takin' over. 'Course, some stood up to him -- an' he killed 'em. Horribly. One o' the only safe places left was Hogwarts. Reckon Dumbledore's the only one You-Know-Who was afraid of. Didn't dare try takin' the school, not jus' then, anyway."

I'm sure there were many other wizards, particularly when people still though Voldemort was gone, who were willing to say Voldemort's name, but simply very reluctant to do so. The setup would be very similar. Young children would wonder why, for example, their relatives were dead. (Remember that many wizarding families lost relatives in the first war in Britain). Then their parents would have to tell them, and would reluctantly hand over Voldemort's name.

Don't forget: Voldemort is a constant topic of conversation.

When a massive war happened barely a decade before, the phrase "You-Know-Who" will be on everyone's lips. Once a child has picked up a modicum of language, it would only be natural to say, "No, I don't know who." And then their parents have to explain to them in hushed voices who they are actually talking about, and not to say his name. Most people, I imagine, were not so devoted to not saying Voldemort's name that they would refuse even to whisper it to their children. I suspect that most people could write it down, to start with.

And that's really the answer: Voldemort is someone that you need to know about. People may use euphemisms, but they know his real name. It's a bit like how people often used to say "passed away" instead of died, almost uniformly, for the sake of politeness, but everyone still knew the name of death.

Answer 2

The Taboo was placed after the ministry fell in book seven. Before that there was nothing preventing people from saying the name, save general superstition.

Now they’ve put a Taboo on it, anyone who says it is trackable — quick-and-easy way to find Order members! They nearly got Kingsley —”
_{(Harry Potter and the Deathly Hallows - Chapter 20)}

To quote Richard, We can assume that children would learn about "Voldemort" the same way they learn other "unspeakable words" such as swearwords and racial epithets.

By hearing them said by those who don't care about the consequences, by reading them in books and literature aimed at adults and by hearing them spoken by adults when they don't think children are listening.