Same reason Cumberbatch was "John Harrison" until Khan name drop. There's probably no practical reason other than a "ohhhh!" moment for the vast minority of the audience who knows who Plagueis is.
Not sure why he'd bother. Palpatine had something to protect. Vader did not, so he went by Darth Vader. This Plagueis guy, what would he be protecting? I mean, why would he need any sort of code name?
Anyway, I just wanted to suggest Snoke is likely someone's relative. I'm not that big into Star Wars that I'd care overmuch to continue this argument.
Well, in universe, John Harrison was John Harrison because they needed to give him a code name as to not reveal that Starfleet is employing the genetic Superhitler named Khan as a researcher for their weapons programs.
Similarly, calling himself "Darth Plagueis" would maybe be a bad move as:
* You're supposed to be dead, killed in your sleep by your apprentice, which is kind of an embarrassing way to go
* You're using a name that is unmistakably a Sith name. Who knows, maybe the Stormtroopers and lower commanding officers of the First Order don't even know their "Supreme Leader" (a perfectly 'worldly' title) is some sort of dark Jedi. For all we know, nobody beyong Hux and Ren might have actually ever seen his appearance.
The speech about wiping out the republic and becoming the new de facto power to rule the galaxy is held by Hux, not Snoke, too. So i guess he's not the most 'visible' of leaders.
What Plagueis "protected" was the fact that, once again, a Sith might be pulling the strings of the 'new Empire'. Similar to the Emperor, who eventually failed.
I wonder how the First Order actually handles Palpatine's legacy. Whether he's being idolized as the former great leader or dismissed as an eventual failure.