"Hi, it's Amiga Inc here, our security certificate has run out. Can you renew it please and send us the bill" and Starfield said "Yes, Bill, we'll do that right away"
This may apply for any other service, but a security certificate is a statement about who you are. This statement is not accessory to the service, but rather this is what the service, and what you declare, and what is verified, are all about. If you cannot even state properly who you ("us") are, then I would say that you have a problem. And if you call a certification authority pretending that you are Amiga, Inc. (Washington) when instead you know that you are Amiga, Inc. (Delaware), an unrelated company, then that could even be considered something like fraud, I guess.
Of course, this may be bordering conspiracy theory, but think about it for a moment, because it could even make sense: maybe they can't change the certificate, because their little secret is that the new Amiga, Inc. (Delaware) does not own the domain amiga.com. So they can only renew it by pretending that they are the dead company. Which, according to whois data, is the owner of the amiga.com domain. I don't think this is peanuts. People know how much a domain like this is worth, especially if they care so much about "intellectual property", and if they carefully transferred things from one company to the other in several steps. So, I'd be curious to know what is behind this. If it was just a mistake, it could confirm how everybody treated the two companies as if it were one, which is also a bad thing to do, when you are trying to avoid legal and financial problems by setting up a new and "unrelated" company. Certainly, by running two businesses with the same name, as they are doing now out of two states, and even providing and renewing services for each other, and in particular doing so on such important things like your web presence and your digital identity, you don't help support the "unrelated" claim.