If you're asking if these are the alternate names of Death Star, then no.
They seem to be separate projects, based on Alexander Freed's official RO novelization:
She spoke sternly, demanding Cassian’s attention as she read from the screen. “Project code names: Stellarsphere. Mark Omega. Pax Aurora…” Were all of them weapons like the Death Star, designed for terror and genocide? Had her father known about the others? She couldn’t afford to think about it—there were too many horrors down that road. “War-Mantle. Cluster-Prism. Black-Saber.”
(Chapter 19)
Note that these were code names for different projects, with different physical cartridges - not simply discarded names from Name-This-DS1-project game:
The cartridge was unlabeled, no different from any other. No different from the thousands surrounding her, except that her father had given his life to reveal it.
She wedged a boot against the stack for leverage, set a free hand on the handle of Mark Omega or Pax Aurora or Heartchopper or whatever ghastly thing the Empire’s scientists had thought up, and tugged at Stardust in the hand of the machine. The frozen arm clung tight; then she jerked the tape away and the arm bobbed loosely in the air.
However, as this answer by Jason Baker indicates, they may possibly have been separate projects that were covering pieces of technology in DS sub-components (tractor beams, hyperdrive etc...)
Ironically, you were right to pick up the point that "Stardust" name is special, though your guess was wrong as to why. Stardust has nothing to do with what remains after Death Star shoots. It's an affectionate childhood nickname Galen had for his daughter Jyn.
“I love you, Stardust.”
“I love you, too, Papa.”
(Prologue)
Papa looked at her kindly. Jyn thought she’d surprised him, in a good way. “Stardust. Don’t ever change.”
(Chapter 3)
and that's how she knew which file she needed:
And she stopped.
The next name stood out with burning intensity, so obvious she might have found it by touch.
“What?” Cassian asked.
“Stardust,” Jyn said. “It’s that one.”
“How do you know that?” Curiosity and urgency mixed in his voice, as if he wanted to say: Be sure.
Jyn was sure. “I know because it’s me.”
Cassian looked at her with astonishment. Then he turned back to the console, gripped the controls fiercely. “Kay, we need the file for Stardust!”
(Chapter 19)
