Jedi have understudies called Padawans. What is the Sith equivalent of a Padawan?
In T and C-Canon, prior to Darth Bane's reformation of the Sith order, they were referred to as Sith Acolytes.
Sith Acolyte was a rank within the Sith Order prior to Darth Bane's reformation. The term was used to refer to Force-sensitive apprentices who had only just started on the dark path under the tutelage of a more experienced Sith Lord.
After the reformation, they are referred to as Sith Apprentices, or just "Apprentices".
A Sith apprentice was an individual (and on occasion, a child), that began serious training under a Sith Master, usually chosen by the Master himself or herself, after the potential apprentice displayed an impressive act of loyalty or cruelty.
There is no indication that Sith Apprentices are officially called anything but exactly that in G-Canon.
StarWars.com refers to them as such.
One Sith had the cunning to survive. Darth Bane restructured the cult, so that there could only be two -- no more, no less -- a master, and an apprentice.
In The Phantom Menace, Sidious refers to Maul as his "apprentice" twice:
DARTH SIDIOUS : (Cont'd) ...Viceroy, this is my apprentice. Lord Maul. He will find your lost ship.
DARTH SIDIOUS : You have been well trained, my young apprentice, they will be no match for you. It is too late for them to stop us now. Everything is going as planned. The Republic will soon be in my command.
He uses the term repeatedly, in Revenge of the Sith
DARTH SIDIOUS: His death was a necessary loss, which will ensure our victory. Soon I will have a new apprentice . . . one far younger and more powerful than Lord Tyranus.
PALPATINE: He became so powerful . . . the only thing he was afraid of was losing his power, which eventually, of course, he did. Unfortunately, he taught his apprentice everything he knew, then his apprentice killed him in his sleep. (smiles) Plagueis never saw it coming. It's ironic he could save others from death, but not himself.
PALPATINE: You are fulfilling your destiny, Anakin. Become my apprentice. Learn to use the dark side of the Force.
PALPATINE: Because the Council did not trust you, my young apprentice, I believe you are the only Jedi with no knowledge of this plot. When the Jedi learn what has transpired here, they will kill us, along with all the Senators.
DARTH SIDIOUS: You have done well, Viceroy. When my new apprentice, Darth Vader, arrives, he will take care of you.
DARTH SlDIOUS: Good . . . good . . . You have done well, my new apprentice. Do you feel your power growing?
RotS also includes a number of instances where the Jedi refer to a Sith "apprentice", but one could argue that they don't know any better.
Finally, in Return of the Jedi:
EMPEROR As you can see, my young apprentice, your friends have failed.
Based on other references from questions on this site, they would simply be called apprentices.
See this question for more details.