We see in "The Deathly Hallows" that Death Eaters were able to track down people who said You-Know-Who's name aloud.
Is it known when the spell to do so was placed?
Was it after the death of Dumbledore? After they took over the Minister's aid? After they took over the Ministry and killed Scrimgeour?
If we trace the dialogues of the characters from the start of The Deathly Hallows up to the chapter A Place to Hide (in the shabby cafe near Tottenham Court Road), there were many instances where the characters mentioned Voldemort but they weren't found immediately by Death Eaters. To cite:
“You claim,” said Uncle Vernon, starting to pace yet again, “that this Lord Thing—”
“—Voldemort,” said Harry impatiently
In the dialogue between Harry and Vernon, Harry mentions Voldemort at least twice. Hestia, one of the OoTP members assigned to escort the Dursleys mentions him once.
Harry sat up too quickly: Lights popped in front of his eyes and he felt sick and giddy. “Voldemort—”
“Easy, now,” said Ted Tonks
Voldemort's name is mentioned many times during the main characters' stay at the Burrow.
"..I don’t know what happened to anyone else, four of them chased us, it was all we could do to get away, and then Voldemort caught up with us—"
(Harry to Molly)
“We’ve been betrayed. Voldemort knew that you were being moved tonight and the only people who could have told him were directly involved in the plan. You might have been an impostor.”
(Lupin)
“None of the Order would have told Voldemort we were moving tonight,”
(Harry)
“Interesting theory,” said Harry. “Has anyone ever tried sticking a sword in Voldemort?..."
(Conversation with Scrimgeour, The Will of Albus Dumbledore)
--
“We know what’s going on! Voldemort’s taken over the Ministry, what else do we need to know?”
(Hermione in the shabby cafe in Tottenham Court Road, A Place to Hide)
Within minutes after Hermione delivers the dialogue above, Dolohov and Rowle find the trio.
Therefore, it's safe to assume that the Taboo was implemented immediately after the Death Eaters seized control of the Ministry or after they killed Scrimgeour (at the end of the chapter The Wedding).
But then again, if you look at the instances above, Voldemort's name was mentioned in places with very powerful protective enchantments (i.e. 4 Privet Drive, the Burrow, Tonks' home). Thus, it's also possible that the Taboo was already in place, but that it may not have been powerful enough to break the enchantments at those locations.
It's not explicitly stated exactly when Voldemort put a taboo on his own name, but I would guess it was before the Ministry falls in the beginning of Deathly Hallows, as Voldemort is on the verge of seizing control of the Ministry. We know the name is Taboo when Harry, Ron, and Hermione escape Bill and Fleur's wedding (which occurs as the Ministry falls) to Tottenham Court Road. While sitting in a cafe, Hermione says "Voldemort" and Rowle and Dolohov, the Death Eaters, show up dressed as workmen and attack the trio within perhaps 20 minutes of them leaving the wedding. The taboo is referenced in canon:
Ron was now filling Harry in on everything he had discovered about the wider wizarding world during his weeks away.
‘... and how did you find out about the Taboo?’ he asked Harry, after explaining the many desperate attempts of Muggle-borns to evade the Ministry.
‘The what?’
‘You and Hermione have stopped saying You-Know-Who’s name!’
‘Oh, yeah. Well, it’s just a bad habit we’ve slipped into,’ said Harry. ‘But I haven’t got a problem calling him V—’
‘NO!’ roared Ron, causing Harry to jump into the hedge and Hermione (nose buried in a book at the tent entrance) to scowl over at them. ‘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!’
‘Because we used his name?’
‘Exactly! 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! They nearly got Kingsley –’
Deathly Hallows - Page 316 - British Hardcover - Adult Edition
and:
‘Come on, Hermione, why are you so determined not to admit it? Vol—’
‘HARRY, NO!’
‘—demort’s after the Elder Wand!’
‘The name’s Taboo!’ Ron bellowed, leaping to his feet as a loud crack sounded outside the tent. ‘I told you, Harry, I told you, we can’t say it any more – we’ve got to put the protection back around us – quickly – it’s how they find –’
Deathly Hallows - Page 316 - British Hardcover - Adult Edition
and:
‘You know who used to like using the Dark Lord’s name, Weasley?’ growled Greyback. ‘The Order of the Phoenix. Mean anything to you?’
‘Doh.’
‘Well, they don’t show the Dark Lord proper respect, so the name’s been Tabooed. A few Order members have been tracked that way. We’ll see. Bind them up with the other two prisoners!’
Deathly Hallows - Page 364 - British Hardcover - Adult Edition
OK, since nobody else stepped up to the bat with a better idea:
As per HP Wikia article on "Taboo" spell:
Sometime after seizing indirect control of the Ministry of Magic in 1997, Voldemort made his own name Taboo.
However, this doesn't seem to be backed up by any specific in-Universe resources I'm aware of other than common sense and logic.
It doesn't make sense.... They got attacked in Tottenham Court Road but not while hiding at Sirius' house in the chapter Magic Is Might (pg 234).
"Dumbledore wanted you to use Occlumency! He thought the connection was dangerous - Voldemort can use it!"
Later on, Ron states the name is Taboo and that all protective enchantments will be broken upon using Voldemort's name.
