IMHO Microsoft 365 is a huge step forward in IT Support for small business. But the name MS has chosen for it is a disaster.
We consultants will have to waste so much time explaining the difference between Office 365 and Microsoft 365 to decision makers in the SMB sector that hardly know the difference between Windows, Office and Microsoft. Look what happens if you type Microsoft 365 or even "Microsoft 365" in a search engine. Even Bing sends you to the Office 365 login page. Change the product name, while you still can! The current name could kill it.
Knowing marketing-people I understand the idea behind the name, well, a bit. But they did not look outside their narrow marketing strategy box. There's people out there in the swamps that have to support your products to make them work, you know. Please, please, choose names for your products that refer to their functionality. You're not selling diapers or soda.
Please, please, Microsoft, if you hire new people for your marketing department, send them off for a one year intern on a helpdesk first.
If you have to explain the difference between the two I would question if you use the Microsoft product as a product or as a way to achieve something, to fix a problem. I couldn't care less about the product name. I wouldn't sell intune but a service that does remote management of your desktops, intune is just the means to an end. Just my two cents. Nothing can kill Office 365, especially not the product name. It is a multi billion service. I doubt that the name has an impact.
You're at the sharp end, so you probably have more of a perspective but I don't think there is anything wrong with the name per se more the material used to explain the offerings isn't that effective. I mean Secure Productive Enterprise wasn't exactly inspiring as names go, at least Microsoft 365 ties in with a few things, like Office 365.
Unfortunately, the best materials I have seen that's much better explaining Microsoft 365 is for partners only and not for the public. There are so many combinations, like all the add-ons available to Microsoft 365 Business, having to work it out is almost impossible otherwise. I don't think they need to change the name just have better guidance on what it is, how it compares to the rest, what it isn't etc, oh having a trial easily available wouldn't hurt either. The official documentation is ok but there still seems something missing.
I think every time you bundle products together the naming is not easy.
If you make it something simple then you have to explain in detail what it is.
Explaining office 365 to anyone is not easy. Let alone adding EMS. The Windows licenses is pretty standard.
Describing a package of tools in a name for marketing gets very wordy fast and not good for marketing. I certainly have a problem finding a good new name for it . You could add a tag line under the name. Productivity tools in a package. Windows 10, Office 365 with Enterprise Mobility and Security features.
Anyway I am no marketing expert as you can tell. However a simple name is just an opener as people instantly ask the question, what is it? Which opens the conversation.