Since we are even further off topic..... ha ha ha.... I'll keep it moving that way.
Needs Discussed Again
It seems to me that calling software by the name of the software (not the company name) is the standard. Nobody seems to use the full name, they just say the product name to save time and effort, I guess.
Image-Line FruityLoops, PreSonus Studio One, Cockos Reaper, Steinberg Cubase, Apple Logic, Bandlab Cakewalk, or Avid Pro Tools. Same with plugins.... Antares Audio Technologies Auto-tune or just plane Auto-tune? I'll bet you most people between 20-50 years old know what Auto-tune is, but wouldn't know what Antares is. This isn't just in the DAW world, either. Do we refer to it as Microsoft Window or do we just say Windows? Intuit TurboTax or just TurboTax? Adobe Photoshop or just Photoshop?
So calling Ableton Live simply "Live" makes complete sense to me.