Umbridge didn’t necessarily know - but she wouldn’t have cared.
The Dark Lord didn’t declare himself Minister or in any way announce himself as ruler to the Ministry officials - he took over quietly, so many people didn’t know he’d taken over. He’d said the former Minister resigned, was in the process of convincing the wizarding world Harry was responsible for Dumbledore’s death, and wasn’t showing himself to the public.
“But surely people realise what’s going on?’
‘The coup has been smooth and virtually silent,’ said Lupin. ‘The official version of Scrimgeour’s murder is that he resigned; he has been replaced by Pius Thicknesse, who is under the Imperius Curse.”
- Harry Potter and the Deathly Hallows, Chapter 11 (The Bribe)
There were some people who suspected that the Dark Lord was behind the sudden and drastic change in Ministry policy, though.
“He doesn’t need to, Ron. Effectively he is the Minister, but why should he sit behind a desk at the Ministry? His puppet, Thicknesse, is taking care of everyday business, leaving Voldemort free to extend his power beyond the Ministry.
‘Naturally many people have deduced what has happened: there has been such a dramatic change in Ministry policy in the last few days, and many are whispering that Voldemort must be behind it. However, that is the point: they whisper.”
- Harry Potter and the Deathly Hallows, Chapter 11 (The Bribe)
The Dark Lord also didn’t staff his Ministry with known and infamous Death Eaters. He mostly used already existing Ministry officials, by using the Imperius Curse or using ones who were in favor of pure-blood rule without having actually joined the Death Eaters (like Runcorn perhaps). The only actual Death Eater that was in the Ministry under the Dark Lord was Yaxley, who wasn’t a particularly “known” one. He had escaped charges after the Dark Lord’s first downfall, since Snape listed him as one of the Death Eaters who could have attempted to find the Dark Lord but didn’t.
“You ask why I did not attempt to find him when he vanished. For the same reason that Avery, Yaxley, the Carrows, Greyback, Lucius,’ he inclined his head slightly to Narcissa, ‘and many others did not attempt to find him.”
- Harry Potter and the Half-Blood Prince, Chapter 2 (Spinner’s End)
Yaxley was present at Dumbledore’s death, but that could have easily been kept quiet, and likely wouldn’t be something that people would really know. He was a Death Eater, but not one known to the public, so his presence in the Ministry wouldn’t make it obvious to Ministry wizards that the Dark Lord was in control.
We don’t really see much evidence either way indicating whether Umbridge herself specifically knew or suspected that the Dark Lord had taken control of the Ministry. We know she was enjoying the power and the ability to enforce the types of laws she’d always wanted to create - but we don’t know whether she suspected who was ultimately behind it. Either way, she wouldn’t have likely behaved any differently - she was as prejudiced as she was ruthlessly opportunistic.
