The only issue with Studio One's name, in my opinion was that it was on version 7. Studio One 7 sounds weird. Studio Pro 8 sounds normal. Is it generic? Yeah. When you have things like Cubase, Reaper, Bitwig Studio out there that have "unique sounding" names (though I think Reaper is a TERRIBLE name for a studio software...to me, I'd never guess it was a DAW, but would think it was a game or something...).
So in that sense, yes, it might sound Generic. Kind like Pro Tools sounds generic. You know...that other piece of software out there that somehow managed to be considered "the Standard of Studio Software" by industry professionals? I've tried PT. Wasn't for me. My Sweetwater rep told me that he'd be surprised if Studio One (back when it was version 3 was JUST released) didn't become the next contender for becoming the "new standard." And guess what....I don't think he was that far off. I personally know a number of studios that switched from PT to S1.
But then I guess you also have Fruity Loops (which I get why they renamed it to FL Studio)....which makes it sound "kiddie." Glad that Fender changed the name to Studio Pro. Still keeps that more "professional vibe" with a name that actually implies what it does without making someone have to guess....