The Sith name of the emperor is Darth Sidious. As English is not my native language, I wonder if the is any hidden meaning for the name Sidious.
For English speakers it's a really not subtle hint that he's bad and evil. It's like naming a villain "Bad Man". The name Sidious by itself isn't a word, but it's probably derived from the word insidious.
Google defines the word insidious as
Proceeding in a gradual, subtle way, but with harmful effects.
Which is a good description of what Darth Sidious did in the prequel trilogy.
Strictly speaking, "Sidious" means nothing in English. The word insidious is defined as intended to entrap or beguile.
This word in turn comes from a Latin word, sedere, meaning "to sit" (think sedentary). Insidere means "to sit in"...perhaps a reference to eavesdropping or surveillance. The suffix "osus" means "full of" in Latin (just like "ous" does in English), so it's just a short trip from insidiosus to "insidious".
As Jeff noted, Lucas seems to like to drop the first syllable for scary names - Invader to Vader, Insidious to Sidious. Presumably, a Sith who could control fire would be called Darth Flammatory...
It was a form of naming convention, I believe. Darth Vader from the OT was named based on the word 'invader'. Darth Sidious for Episode 1 works the same way from 'insidious'.
This falls apart, however, for Darth Maul and Darth Tyranus.
Edit, additional info:
As has been pointed out in the comments, 'Maul' and 'Tyranus' both wear their meanings on the sleeves, and they were apparently not intended to survive long as Sidious' seconds. Their names were likely chosen offhand or self-chosen, then.
Plutor posited a link that discusses the history of Vader's name. In my opinion, the dismissal of 'invader' as a source is purely offhand, with no real consideration given. At the time the OT was written, Lucas didn't know Vader was Luke's dad, and had no concept of his history. And Anakin DID act as an 'invader' - he acted from within the Jedi to help destroy them. His corruption to the Dark Side began in AotC, and culminated with his invasion of the Temple in RotS.
So there's certainly a case to be made for 'vader' to be shortened from 'invader', in-universe. In-universe, however, there's no sign that it means 'Dark Father'. The language it stems from (purportedly Dutch) isn't stated in the article, and most likely doesn't exist in the SW universe.
It's based on insidious (slow, subtle, gradual harm) and assiduous (constant application & attention to detail until task is finished), combined with the new Sith philosophy — the rule of two — to sit, wait and work in secret at the whole plan to destroy the Jedi (as was the Sith’s original goal).
His character believed he was the Sithari — the chosen one of the Sith, the culmination of 1000 years of Sith evolution. He learned through his prolonged study of Sith history to renew the way the Sith operated.
He cultivated a small but powerful Sith Order to use against the Jedi and entered politics to work in secret (but in plain view as a Senator) to infiltrate the Republic. The discrediting of the Jedi was his whole plot, combined with Order 66 so he was only left with a small number of Jedi to deal with in his rise to power, which he totally orchestrated & manipulated through controlling the war as the villain and the hero by keeping battles even to prolong the war and exhaust the Jedi.
Also so much study of the Dark Side made him pure evil as he was able to train with his master for decades to learn all he could to prepare himself for his plan to become Emperor by gaining power through the illustrious career of starting and controlling outcomes of war, slowly guiding events to align with his plan until he could gain emergency power to execute Order 66. The phantom menace was his beginning as the new improved Sith & mastermind of the Republic.
Naming a Sith is a Skill. Its based on English word describing a certain kind of evil or dark thing. For example : Darth Sidious is short for the word INSIDIOUS, which is a form of evil. As to Darth Maul is short for Malicious, Darth Vader is short for Invader, Darth Tyranous (count dooku) is short for Tyrany. Darth Revan is for Ravenous, Darth Plaguies is short for Plague. Darth Bane is basically BANE itself.. Darth Gravid is short for Gravity, Darth Ramage is short for Damage.
It seemed that Lucas also used portmanteau words, a combination of 2 words, which means that there are 2 meanings packed into one word. Darth for example reminds the words "dark" and "dart" and possibly "death". Sidious seemed to be made up of the words "insidious" and "vicious". As in Lewis Caroll's poem "Jabberwocky", these words carry meaning because they evoke other words.