How is it possible for Umbridge to find out about the Room of Requirement if Harry specifically asked to keep her from finding out about it?

Question

I recently came across this passage in Harry Potter and the Order of the Phoenix, chapter eighteen.

They hurried along the corridor to the place Dobby had described to Harry, a trench of the blank wall opposite and an enormous tapestry depicting Barnabas the Barmy's foolish attempt to train trolls for the ballet.

"Okay," said Harry quietly, while a moth-eaten troll paused in his relentless clubbing of the would-be ballet teacher to watch. "Dobby said to walk past this bit of wall three times, concentrating hard on what we need."

They did so, turning sharply at the window just beyond the blank stretch of wall, then at the man-size vase on its other side. Ron had screwed up his eyes in concentration, Hermione was whispering something under her breath, Harry's fists were clenched as he stared ahead of him.

We need somewhere to learn to fight . . . he thought. Just give us a place to practice . . . somewhere where they can't find us . . .

As we know from Harry Potter and the Half-Blood Prince, the Room of Requirement can hide from the people that the person requesting wants it to hide from. So how is it possible that Umbridge found out about DA in the Room of Requirement and got the scroll of names?

"We needed evidence and the room provided . . . " And to Harry's horror, [Umbridge] withdrew from her pocket the list of names that had been pinned upon the Room of Requirement's wall and handed it to Fudge. "The moment I saw Potter's name on the list, I knew what we were dealing with," she said softly. (Harry Potter and the Order of the Phoenix, chapter twenty-seven)

Answer 1

That's not necessarily how the room works

First of all, in Half-Blood Prince, it's never said that Draco actually was able to stop anyone else from entering the room. The reason Harry was never able to enter is that he didn't know what the room he needed to go to even was:

But, Harry, before you get all excited, I still don’t think you’ll be able to get into the Room of Requirement without knowing what’s there first.
_{Harry Potter and the Half-Blood Prince - Chapter 21 - "The Unknowable Room"}

Furthermore, as we know, the room of hidden things was still open while Draco was in there, as Trelawney was able to enter.

‘Oh, I got in all right,’ said Professor Trelawney, glaring at the wall. ‘But there was somebody already in there.’

‘Somebody in –? Who?’ demanded Harry. ‘Who was in there?’

‘I have no idea,’ said Professor Trelawney, looking slightly taken aback at the urgency in Harry’s voice. ‘I walked into the Room and I heard a voice, which has never happened before in all my years of hiding – of using the Room, I mean.’
_{Harry Potter and the Half-Blood Prince - Chapter 25 - "The Seer Overheard"}

Every time that Harry unsuccessfully tried to go in he was just trying to find Draco, not trying to enter the Room of Hidden things that Draco was using. As such he was unable to enter. When Umbridge came around, she was already informed of exactly what the room was configured to be and so she was able to enter.

The only time we actually see a reference to someone being able to successfully tell the room to block specifically block certain people is in book seven with Neville.

‘And the Carrows can’t get in?’ asked Harry, looking around for the door.

‘No,’ said Seamus Finnigan, whom Harry had not recognised until he spoke: Seamus’s face was bruised and puffy. ‘It’s a proper hideout, as long as one of us stays in here, they can’t get at us, the door won’t open. It’s all down to Neville. He really gets this Room. You’ve got to ask it for exactly what you need – like, “I don’t want any Carrow supporters to be able to get in” – and it’ll do it for you! You’ve just got to make sure you close the loopholes! Neville’s the man!’
_{Harry Potter and the Deathly Hallows - Chapter 29 - "The Lost Diadem"}

However note that this is presented as a new feat, something that Harry was unaware was possible, and something that only Neville could do due to him "really getting" the Room. Also note that this doesn't seem to have actually been proven in practice, and the reason the Carrows couldn't enter could just be that they also didn't know which configuration the room had taken.