On-premises.
"Private cloud refers to a model of computing where resources are delivered as a service over the Internet from a centrally managed data center. On-premise infrastructure management, on the other hand, refers to an approach where an organization manages its own IT infrastructure, typically in-house."
If you host the virtual machines yourself, don't forget you can leverage Azure services - like Azure Arc to bring Azure capabilities, such as Azure POlicy, and Update Management to your self hosted virtual mchines.