Take a look at what vcf is
VMware Cloud Foundation | Leading Hybrid Cloud Platform
"VMware Cloud Foundation is the hybrid cloud platform for managing VMs and orchestrating containers, built on full-stack hyperconverged infrastructure (HCI) technology. With a single architecture that is easy to deploy, VMware Cloud Foundation enables consistent, secure infrastructure and operations across private and public cloud. Increase enterprise agility and flexibility with the hybrid cloud that delivers it all."
VCF is really vsan, nsx, and vsphere setup in a predefined setup that's defined by vmware. that basically follow. If you look at vmware valided designs
What is VMware Validated Design? | VMware
you can build your own if you have separate products. You have other external certifications that you can look at , like
https://flexpod.com/
that have criteria that you need to meet to be certified as a flexpod setup.
The most basic thing you need is a vsphere license and shared host to be able to run virtual machines, and with that you can still use vmware hcx to link the two for a hybrid cloud but there are other options as well
VMware Cloud
So the basic answer is there a lot of potions to have a "private cloud" but it really depends on your use cases for what product you need.
