star wars - Why didn't Palpatine publicly change his name once he became Emperor?

Anakin Skywalker was known as Darth Vader (this was already his Sith name) after the creation of the Galactic Empire.

So why did Palpatine remain "Emperor Palpatine"? Why didn't he embrace his persona as Darth Sidious?

I started wondering after reading one of the answers to "Why was Count Dooku not given word “Darth” in his name?"

Answer

A lot of politics is perception hiding what is really going on. Yes, those close knew well that Palpatine was a Sith, but to much of the general public, those were just stories and rumors of a far away place that had very little to do with them. What happens in the capital isn't their problem or their concern. And people say all kinds of different things about far away people and places. Who's to say what's true and what isn't?

In the end, Sith or not, Palpatine is still a politician and realizes that as long as most of the people think things are relatively the same as always, then far fewer of them will openly rebel against the order of things. So there's more soldiers about? Just means better security and less crime to the people. And for that, they're willing to dismiss a great deal as rumor and speculation by those who don't care for the status quo.

But people still knew what the Sith were from legends and wars of the past. Were he to openly declare himself in a way that validated it to the public at large, there would be far more rebellion than just the Alliance's small force. So by maintaining the public perception that he was just Emperor Palpatine, more of the public will keep in line. It's all about the show.