CerberusGate
I should save my game in a whole new slot
You don't actually need to go out of your way to think up new corporations like that; a nod, a footnote or a reference mentioning them would be enough. It's unnecessary since the story of a Fallout game should focused on the challenges that a post-apocalyptic society may face. As @Deeves puts it, "Your character and his story arc should be in the forefront" rather than the pre-War world. The latter's story ended when the bombs fell so the story should be focused on how the people have attempted to crawl out of the wreckage of nuclear devestation. There's no need to add so many gimmicky additions from pre-War days or be reliant on them.Here's an idea for a vault Tec competitor.
"FROM THE COMPANY THAT GAVE YOU SEA HORSE THE ROBOT ITS,
AQUARIUS PERSONAL NUCLEAR SUBS. NOW FOR THE PRICE YOU CANT AFFORD, YOU CAN PURCHASE YOUR OWN SUBMARINE!
"WOW REALLY?"
Yes little Timmy, now you and your family can live safe from nuclear fallout by living the rest of your life's in the ocean. Experience for rest of your life the smell of clean air, or solid ground. Fear constant repairs that may or may not end your life. Discover fantastic mutated sea creatures that will probably eat your face!
Who needs a vault when your under the sea! And if the seas not hidden enough, too bad your dead then cause you didn't get a vault. So get your own personal submarine today!
(WARNING! Chinese subs will still most likely be in ocean. Personal submarine comes with no weapons and has room for only 6 people in it. Product may cause radiation sickness and depression if stayed in ocean too long. Consult Doctor, or better yet take one to your submarine so you can live the rest of your days in an endless watery abyss.)
So go out and get one! Today!
That's what Fallout 1, 2 and New Vegas did since in those games; the only apparent effect of the pre-War world was the legacy left behind in the wreckage (like the tools and technologies that could be used to better/worsen life or said technologies become folk tales that lure desperate people to their dooms).
Try to keep this quote of Tim Cain in mind:
My idea is to explore more of the world and more of the ethics of a post-nuclear world, not to make a better plasma gun.