If Apple didn't have that policy, would would prevent any old scammer from publishing their own "Netflix" or "Amazon" apps?
Why would your name always be different? Apple's Developer program is designed for developers who write their own apps. They do this under their own names. Would you want to trust your personal data to some anonymous developer?
You are talking about a particular business model - a developer for hire. Apple doesn't support "business models". Apple supports "developers". If you want to do work for a client, the expectation is that the client will hire you as an employee and you will work under your employer's account. If you are a contractor instead of an employee, it is the same thing, just without employee benefits. Apple explicity supports having multiple developers have access to a business account.
You can't just change your account to a business. You have to be a business, then you can create a business account. Then you can attach developers to your account. But none of that would change anything above. The organization developing the app still has to contract with you, the business, instead of you the employee or the independent contractor.
There may be a possibility of getting explicit authorization from a company to use their trademarks and services. I don't know Apple's policies about that. It would be a high-risk to make any assumptions or commitments based on this option.
If you want to be a developer, there are costs to doing business. The $99 yearly Apple Developer program fee should be the smallest of all of your expenses. Your other, monthly expenses should be an order of magnitude higher than that. If that isn't true, then you are a hobbyist and shouldn't be submitting bids to companies to do this kind of work. You need to know how the process works so you can inform your clients about what they will need to do and help them do that legally.
If you're like me, you're out of luck. I think this is theft on Apple's part. I've tried, to no avail, to get a refund on my app that they won't publish. It was a small app for my team to use on a retreat. They denied it (nothing profane) they just didn't want to approve it. Now, I don't have a published app and I'm out $100. Apple is shady and has suspicious business practices.