Renaming isn’t rebranding
The name of your business is just that, a name. It’s the moniker your business goes by. It’s what you put on a business card or an email signature.
The brand of your business is much more than the name. It’s the customer experience. It’s the story you tell. It’s the attitude you project. It’s what a customer expects from you.
A rebrand doesn’t inherently mean a name change. You can do one without the other. (Though it’s more likely that if you are renaming, you probably should consider some degree of a rebrand.)