It's usually called on-premise, private cloud or self-hosted.
On AWS Marketplace you can rent such software per hour (plus the cost of the servers), e.g. https://aws.amazon.com/marketplace/pp/B07KRRSWLY
Other cloud infrastructure providers also have marketplaces, even for free software, because they earn from customers renting their servers. https://marketplace.digitalocean.com/category/developer-tool... https://marketplace.digitalocean.com/category/blogs-and-foru...
Many large SaaS have separate Enterprise products, e.g. Github https://github.com/enterprise or mapbox https://www.mapbox.com/atlas/ It requires a dedicated support team, strong contracts and customers pay a lot extra.