I am aware of my another question Why did Tom Riddle change his name to Voldemort?
This question is different.
Most people in Wizarding World call Voldemort You-Know-Who, He-Who-Must-Not-Be-Named etc. If Voldemort didn't want people to call his name, what was the point of changing his name?
Voldemort wanted people to fear his name (and him), and had no real problem with people saying it. But people were afraid of him, and so avoided saying his name directly. Even his followers called him the Dark Lord.
Saying Voldemort's name aloud during the First Wizarding war could have been dangerous. What if a Death Eater overhead, and marked you for daring to insult the Dark Lord by using his name? What if an Auror or overzealous neighbor overheard, and thought you were in collusion with Voldemort? Hushed tones and pseudonyms seem like a logical choice for a community whose entire existence depends on secrecy.
Bellatrix, perhaps the most open and avid Death Eater of all, obviously wasn't keen on some people saying Voldemort's name:
To Harry: "You dare speak his name?" whispered Bellatrix.
"Yeah," said Harry, maintaining his tight grip on the glass ball, expecting another attempts to bewitch it from him. "Yeah, I've got no problem saying Vol--"
"Shut your mouth!" Bellatrix shrieked. "You dare speak his name with your unworthy lips, you dare besmirch it with your half-blood's tongue, you dare --"
However, some, such as Dumbledore, told people to use Voldemort's name. He didn't condone the use of "You-Know-Who" and the like.
“Call him Voldemort, Harry. Always use the proper name for things. Fear of a name increases fear of the thing itself.”
The reason the Order of the Phoenix refused to say his name in the Second Wizarding War is because of the Taboo curse put on his name.
The wizards and witches that were "brave" enough to say Voldemort's name outright were usually Voldemort's enemies, such as the Order of the Phoenix. The Taboo let Voldemort trace his enemies.
"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 even 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 ---"
