It’s a name that was created for that storyline. Palpatine, much like the term Sith, was used for the OT and its marketing materials. Sidious was treated as his truer name, with Palpatine being more of the disguise.
Not to get too technical, but the name Palpatine was actually first used in the 90’s EU.
No, it was first used in the prologue of the 1976 novelization of Star Wars. So technically the name Palpatine predates any of the films, even if it wasn’t used in a film until 1999.
Aided and abetted by restless, power-hungry individuals within the government, and the massive organs of commerce, the ambitious Senator Palpatine caused himself to be elected President of the Republic. He promised to reunite the disaffected among the people and to restore the remembered glory of the Republic. Once secure in office he declared himself Emperor, shutting himself away from the populace. Soon he was controlled by the very assistants and boot-lickers he had appointed to high office, and the cries of the people for justice did not reach his ears (George Lucas [Alan Dean Foster], Star Wars: From the Adventures of Luke Skywalker (paperback; New York: Del Rey, 1976), p. 1, ISBN 0-345-26079-1.)
That’s actually really interesting. Supports both the idea that George Lucas had it planned out (in that he had a good idea as to Palpatine rose to power) and the idea that George Lucas was making it up as he went along (because he hadn’t yet decided that Palpatine was an evil mastermind).
Also, in the 1983 novelization for Return of the Jedi by James Kahn:
The Emperor sat, regarding this view, as Vader approached from behind. The Lord of the Sith kneeled and waited. The Emperor let him wait. He perused the vista before him with a sense of glory beyond all reckoning: this was all his. And more glorious still, all his by his own hand.
For it wasn’t always so. Back in the days when he was merely Senator Palpatine, the galaxy had been a Republic of stars, cared for and protected by the Jedi Knighthood that had watched over it for centuries. But inevitably it had grown too large - too massive a bureaucracy had been required, over too many years, in order to maintain the Republic. Corruption had set in.