The company name doesn't fit into the tapestry you've woven. It's like that one pesky red thread that sticks out.
I presume it's like my use of the word "Internet" suddenly in VQF. I've contemplated references to some of the other major brands of today, but I'm so far in the future, I can't see any of those companies surviving. My setting experiences (social) entropic loss. This is to say, the broad message is cultures tend to boil down to nothingness over time, barring brief spikes of inserted energy. This is true of the others such as Star Wars where basically tech hasn't much improved in the past thousand years and there seems to be no will to move forward, and Enders Game where it took an alien invasion to get mankind to stir.
Your setting is one of renewal where old things become new again. This is quite unusual in sci-fi (quick: name all the movies/shows in the last 30 years with a greco-roman, mayan/aztec, Prussian, Babylonian, you-name-the-empire cast in space. Done? Off the top of my head, I only came up with Star Gate). As a result of this scarcity, you're going to have to do unusual things like have a company called Acme.
Side note: In VQ, Arkaya Corp is my equivalent of Acme. They made the droids that hunt Andrea down in her chapter one, and run the waste disposal company in Laurie's story. They so this and much more through a vast series of subsidiary companies. I've devoted significant page space to joining all these companies up, but you might want to go that route if you decide against Acme.
As for chapter one, my thoughts of the AI remain the same. I haven't commented that because I don't want to prompt you into an editing spree on a chapter one. Not until you write those other words "the end". I think a good chapter one is finalized after the last chapter is set in stong. The two chapters should reflect each other in theme, style & tone (reflect -- not rival)
Hope this helps