The product name is not specific to on-premises. What you describe is the difference in licensing between on-premises and cloud. Microsoft didn't make it easy for us.
So does "Dynamics 365 Finance and Operations" refer to the on-prem implementation, while just "Dynamics 365" or "Dynamics 365" followed by individual module "Supply Chain Management", "Finance", "Commerce", "Human Resources" or "Project Operations" refers to the cloud implementation?
What would you like to call it? :) I have clients who call it MSD, Dynamics, D365, F&O, FinOps, Finance & Operations, UO, Unified Operations. Whatever its official name is today, you can be sure MSFT will change it soon - LOL.
Can you tell why you are asking this question? Many different persons do have their own view on product names. Microsoft doesn't make it easy for us.
Dynamics 365 Finance and Operations is still Dynamics 365 Finance and Operations.
Microsoft had split the licensing for the cloud version into multiple SKUs, like Finance, Supply Chain Management, and Human Resources.
Some people are also talking about Dynamics 365 Finance and SCM, but that does not cover all apps and features of Finance and Operations.
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