Is there any customization which can be applied to the default "Install" button in the custom installation page ? Such as changing its display name to "Next" until the user reaches the last stage of the setup. Or to remove it completely until custom validation is done.
The default Install button cannot be changed. You can, however, add whatever buttons you need and multiple pages to the setup screen as you like within the custom installation page. The last step of the flow will be clicking on the Install button on the bottom of the page.
Please refer to this app https://www.freshworks.com/apps/freshservice/contract_hour_manager/. You'll see how this can be achieved at the moment.