Renaming your company is a paperwork-intensive process - you need to provide proof to Apple that the new name is registered as a company and owned by you.
Thanks for the link. How does company/organization name work when one doesn't have an LLC or anything else "official"? Perhaps one can just use their name.
Details: https://developer.apple.com/support/ios/account-management.h...
(Giving your app a new name is trivial, on the other hand, and can be done when submitting an update in iTunes Connect.)