Darth Prodigium, Latin for Prodigious.
He would not be trained by Vader, but by Sidious. With Luke's great innate arcane talent, and by virtue of being stronger in the Force than perhaps all but his father - he would indeed be a prodigious Sith Lord.
With Sidious' similar prodigious nature, and the knowledge they'd hold, Luke would become one hell of a Sith Lord under Sidious' tutelage he'd learn to be more self-sufficient, and his force of will would be greater, he'd be willing to go to any extreme to conquer his goals.
Darth Whomp Rat!
Originally posted by Kickballjedi
Luke becomes the Clone Palpatine's apprentice is Dark Empire, does he receive a Darth name at that point?
No, that was before it was revealed that Darth was a common sith lord thing and not just a Vader thing.
It's not until the prequels and Maul that we started having more Darths (Palpatine wasn't known to be Sidious yet).