When Harry and Lupin had a chat in Lupin's office on the first Hogsmeade trip in the Prisoner of Azkaban, Harry asked why Lupin didn't let him have a turn with the boggart that they had done a few days ago. Lupin's reply was that he was afraid that it might have turn to Voldemort. This surprised Harry, as at the time he and Dumbledore were the only ones who consistently said Voldemort's name out loud.

What made Lupin specifically unfazed by the usage of the name? Was it because Sirius Black was on the loose and (at the time) thought it would make him seem intimidating to him if they reunited?

He has been the member of the Order of Phoenix since the first war with Voldemort. And as we know from Harry Potter and the Deathly Hallows - members of OoP are not afraid of using Voldie's name, which is the reason some of them even get caught, as Greyback mentioned.

"Left, 'ave you, ginger?" said Scabior. "And you decided to go camping? And you thought, just for a laugh, you'd use the Dark Lords name?"

"Nod a laugh," said Ron. "Aggiden."

"Accident?" There was more jeering laughter.

"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!"
_{Harry Potter and the Deathly Hallows, chapter 23, Malfoy Manor}

Moreover, Lupin was one of the greatest Dumbledore's followers, and we all know what Dumbedore says about using "You-Know-Who" instead of his name.

"Call him Voldemort, Harry. Always use the proper name for things. Fear
of a name increases fear of the thing itself."
_{Harry Potter and the Sorcerer's Stone, chapter 17, The Man with Two Faces}

Dumbledore encouraged his allies to use it.

Dumbledore encouraged those around them to use the Dark Lord’s name. He tells McGonagall that he’d been trying to convince people to call him by his proper name for eleven years.

"My dear Professor, surely a sensible person like yourself can call him by his name? All this 'You-Know-Who' nonsense – for eleven years I have been trying to persuade people to call him by his proper name: Voldemort." Professor McGonagall flinched, but Dumbledore, who was unsticking two sherbet lemons, seemed not to notice. "It all gets so confusing if we keep saying 'You-Know-Who'. I have never seen any reason to be frightened of saying Voldemort’s name."

"I know you haven’t," said Professor McGonagall, sounding half-exasperated, half-admiring. "But you’re different. Everyone knows you’re the only one You-Know – oh, all right, Voldemort – was frightened of.”
_{^{- Harry Potter and the Philosopher's Stone, Chapter 1 (The Boy who Lived)}}

Dumbledore also tells Harry to use the Dark Lord’s name because fear of a name increases fear of the thing itself.

"Sir?" said Harry. "I’ve been thinking … Sir – even if the Stone’s gone, Vol– … I mean, You-Know-Who –"

"Call him Voldemort, Harry. Always use the proper name for things. Fear of a name increases fear of the thing itself."
_{^{- Harry Potter and the Philosopher's Stone, Chapter 17 (The Man with Two Faces)}}

Dumbledore founded and led the Order of the Phoenix.

"Is anyone going to bother telling me what the Order of the Phoenix –?"

"It’s a secret society," said Hermione quickly. "Dumbledore’s in charge, he founded it. It’s the people who fought against You-Know-Who last time."
_{^{- Harry Potter and the Order of the Phoenix, Chapter 4 (Number Twelve, Grimmauld Place)}}

It’s likely he encouraged the Order to use the Dark Lord’s name as well, because Greyback mentioned that the Death Eaters were able to track the Order by tracing the use of the name “Voldemort”.

"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."
_{^{- Harry Potter and the Deathly Hallows, Chapter 23 (Malfoy Manor)}}

Lupin was in the Order - he was allowed in meetings for Order members only.

Harry made to follow Lupin, but Mrs. Weasley held him back.

"No, Harry, the meeting’s only for members of the Order."
_{^{- Harry Potter and the Order of the Phoenix, Chapter 4 (Number Twelve, Grimmauld Place)}}