Dumbledore encouraged people to call him Voldemort, rather than You-Know-Who, because there was a lot of fear not just of Voldemort, but merely saying his name. If Dumbledore can remove that then when Voldemort returned - as Dumbledore suspected he would - there would hopefully be a lot more people willing to stand against him.

“Sir?” said Harry. “I’ve been thinking… sir — even if the Stone’s gone, Vol-, I mean, YouKnow-Who —”

“Call him Voldemort, Harry. Always use the proper name for things. Fear of a name increases fear of the thing itself.”

_{Philosopher's Stone, Chapter 17 - The Man With Two Faces}

So, why not encourage them to call him by his real name? It's still essentially a crutch; you're replacing one name they're not afraid of ("You-Know-Who") with another name they're not afraid of ("Tom Riddle"). Everybody knew him as Voldemort, that's the name that all the fear - and therefore power - is attached to, and that's what Dumbledore needed to break.

I do, however, find it interesting that in the first book Dumbledore says "Voldemort" is the "proper name" for him, yet insists on calling him Tom in every interaction (I can think of) between them in the later books. I suppose Dumbledore's not against trying to get in Voldemort's head, and knows that he hates anything connecting him to his Muggle past.

Good question! I expect it's because J.K.Rowling is only human, but you could argue that it's because hardly anyone knew Voldemort used to be known as Tom Riddle ^[1]. Even if Dumbledore told them, it's unlikely they'd believe him, or even remember the name.

Plus, people were afraid of the name Voldemort. Telling people to refer to him as "Tom Riddle" is just another euphemism, much like "you-know-who", meaning people would still be afraid of the name "Voldemort".

Dumbledore wanted to encourage people not to fear the name "Voldemort" specifically because that's the name that made them scared.

I think Dumbledore had the highest priority having Voldemort confident about his horcruxes secrets being kept.

Spreading Voldemort's childhood would have most likely put attention on early crimes he committed, and to places/facts connecting to actual horcruxes. He would then have put much security on them. And Dumbledore's plan relied on Voldemort being overconfident about his secret's safety.

Also, I would point the argument already answered in this thread("anonymous"):

Dumbledore was likely just acknowledging this transformation, which was to be expounded upon in later books. Even if Dumbledore knew that there was part of Tom that still existed in Voldemort, this person was not the Tom he knew and had previously chosen to become a student.

Voldemort seems to be styled after Satan. Some believe that Satan's name changed from Lucifer (or something other than Satan) to Satan after the fall (due to a few possible misunderstandings mentioned below). This can be paralleled to the name change from Tom Riddle to Voldemort, which also indicated a transformation from the student Tom Riddle, who was part of the larger wizarding community and the student body of Hogwart's, to Voldemort, as part of his split to lead an opposing force (the Death Eaters).

Dumbledore was likely just acknowledging this transformation, which was to be expounded upon in later books. Even if Dumbledore knew that there was part of Tom that still existed in Voldemort, this person was not the Tom he knew and had previously chosen to become a student.

Also, the wizard formerly known as Tom Riddle was calling himself Voldemort and most people knew him as Voldemort and not Tom, so it made sense for Dumbeldore to call him Voldemort.

More info:

In World Book Day Chat in 2004, Rowling acknowledged ^[1] that Voldemort is not based on any (living) person: "lol No I didn't base Voldemort on any real person!" Additionally, Rowling stated ^[2] in a later interview, '"To me, [the religious parallels have] always been obvious," Rowling said. "But I never wanted to talk too openly about it because I thought it might show people who just wanted the story where we were going."'

Isaiah 14:12 starts with a modern translation of "How you have fallen from heaven, morning star, son of the dawn!", but in the King James Version this was translated as, "O Lucifer, son of the morning!" (Lucifer meaning light-bearer, another name for the morning star, Venus). Though this was written about a king of Babylon, (possible) misunderstanding (seems to have) led to Lucifer becoming one of Satan's names. Since Satan is a verb meaning primarily to "obstruct or oppose", one might believe that Lucifer was "renamed" Satan after his fall from Heaven, because it was his opposition that caused his fall, and some have this belief. Whether or not Rowling believed that Satan's name changed from Lucifer to Satan or whether she was just aware of his various names and surrounding literature, this may have had influence on Voldemort's back-story.

This is highly speculative. In the event of his return, having a great many wizards referring to you-know-who as Voldemort would render the taboo on his name useless.

Perhaps Dumbledore was simply planning ahead trying to take away Voldemort's central tool for identifying adversaries.

Dumbledore uses Voldemort's given name to humble him. As Tom Riddle he is no longer the Dark Lord, but just another former student.

In the first book (if you don't believe Rowling had the whole story figured out from the beginning) the obvious answer is that Dumbledore wanted to demystify Voldemort by having people refer to him with his "real" name and therefore make him seem more like a real threat that could be dealt with. The exchange between Dumbledore and Harry in the ward emphasizes this, where Dumbledore tells him that fearing the name makes you fear the person.

When Dumbledore later calls Voldemort "Tom" in their encounters it always seemed to me like he was doing it to mock him. To trip him up and have him make a mistake by reminding him of their previous relationship, and that no matter how far he's gone, Voldemort still used to be that unwanted bastard child. I doubt Dumbledore would have put it like that, but he's definitely reminding Voldemort of his past by calling him Tom.

Voldemort's past is shrouded in mystery for almost everyone except Dumbledore and possibly the rest of the Order. Perhaps it would have been a good tactic to spread the knowledge of Voldemort's childhood and origins, and then start telling people to call him Tom Riddle, but that's a multi part strategy that Dumbledore & Co might not have felt warranted their time and effort instead of something as simple as telling people to stop whispering pseudonyms in the night.

I will give you an example from real life.

Edison Arantes do Nascimento is better known as Pele. Everybody has heard of Pele. But there is rarely someone who knows his real name.

So according to you: is there someone out there who can possibly think that encouraging people to call Pele Edison Arantes do Nascimento would be worth the effort?

He didn’t want to widely reveal his knowledge of the Dark Lord.

Dumbledore wouldn’t have told everyone to call the Dark Lord “Tom Riddle” because he didn’t want the extent that he knew of the Dark Lord’s past known. That was likely to keep him confident in how well his secrets were hidden, so he wouldn’t suspect Dumbledore knew of the Horcruxes and decide to increase their protection. When Dumbledore started telling Harry about the Dark Lord’s past, he also told Harry to make sure no one else would know other than Ron and Hermione.

“Sir, am I allowed to tell Ron and Hermione everything you’ve told me?’

Dumbledore considered him for a moment, then said, ‘Yes, I think Mr Weasley and Miss Granger have proved themselves trustworthy. But, Harry, I am going to ask you to ask them not to repeat any of this to anybody else. It would not be a good idea if word got around how much I know, or suspect, about Lord Voldemort’s secrets.”
_{^{- Harry Potter and the Half-Blood Prince, Chapter 10 (The House of Gaunt)}}

Dumbledore didn’t want it known how much he knew - so he wasn’t going to tell the rest of the wizarding world to call the Dark Lord “Tom Riddle”. It wouldn’t have helped them much (a Dark Lord by any other name can still cast Killing Curses at those who defy him) and it went against Dumbledore’s “master plan” to show how much he knew.

Dumbledore was not without pride, and he considered his part in Tom Riddle's rise to power as one of his greatest failures. Whatever his rational reasons are for keeping Voldemort's past in the dark, one reason was to protect himself, and, perhaps more importantly, Hogwarts.

Harry was not burdened by the past, and in fact was intentionally kept in the dark about many matters of the past so as to position him in such a way that he wouldn't be held back by the past, as Dumbledore, Snape, and many, many others were. Thus he had no reason to not use Tom's name, but as the wizarding world knew Tom as Voldemort, it would only be confusing if he were to use it widely. Thus he only used it with Tom himself. The more you know about a thing, the more power you have over it, and Harry used Tom's name to demonstrate that he knew things Tom wanted to keep hidden.

The reason that Dumbledore wanted people to use "Voldemort" as his real name in the first book and then calls him Tom in later books is because "Tom Riddle" had yet to be introduced in the series yet. If Dumbledore had referred to him as Tom in the first book before Tom's "story" was introduced, it would have been more confusing than if he calls him Tom in later books. Also, there were very few people in the wizarding world who knew Voldemort's true name (assuming that Prof. McGonagall wasn't teaching when he was at Hogwarts) so it's best to assume that until the story behind Tom Riddle was thought of, it would be best for Dumbledore to call him Voldemort.

I believe that Dumbledore doesn't want people to fear the name "Voldemort" for obvious reasons stated above and asking them to call him Tom is yet another name instead of using you-know-who.Dumbledore calls him Tom because he disregards the name Voldemort ,he doesn't think much about Riddle's avatar except that he his a sorely misguided wizard using his powers for evil instead of the good ,however as people regard Voldemort with fear he encourages them to get over that fear and start calling him Voldemort