Quite a few Order members use the name.
Albus Dumbledore
“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).
Rubeus Hagrid
“Could you write it down?” Harry suggested.
“Nah - can’t spell it. All right - Voldemort.” Hagrid shuddered.
(Philosopher's Stone, Chapter 4, The Keeper of the Keys).
Sirius Black
Black started to laugh, a horrible, mirthless laugh that filled the whole room.
“Voldemort, teach me tricks?” he said.
(Prisoner of Azkaban, Chapter 19, The Servant of Lord Voldemort).
Mad-Eye Moody
“That’s Dumbledore’s brother, Aberforth, only time I ever met him, strange bloke...That’s Dorcas Meadowes, Voldemort killed her personally...Sirius, when he still had short hair...and...there you go, thought that would interest you!”
(Order of the Phoenix, Chapter 9, The Woes of Mrs Weasley).
Hestia Jones
“Doesn’t matter?” repeated Hestia, her voice rising ominously. “Don’t these people realise what you’ve been through? What danger you are in? The unique position you hold in the hearts of the anti-Voldemort movement?”
(Deathly Hallows, Chapter 3, The Dursleys Departing).
Remus Lupin
“I’m sorry, Harry, but I had to check,” said Lupin tersely. “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.”
(Deathly Hallows, Chapter 5, Fallen Warrior).
Bill Weasley
“We saw it,” said Bill; Fleur nodded, tear tracks glittering on her cheeks in the light from the kitchen window. “It happened just after we broke out of the circle: Mad-Eye and Dung were close by us, they were heading north too. Voldemort - he can fly - went straight for them.
(Deathly Hallows, Chapter 5, Fallen Warrior).
That's enough to surmise that most Order members would be comfortable using the name and that people like Minerva McGonagall and Severus Snape were the exception.
We don't have evidence for all the Order members. Other characters either don't use the name or we don't have enough information to say.