Once a project has been created, you can choose to rename, duplicate, fork or transfer it from the "..." menu:
This adjusts the display name of the project but will have no effect on the URL or DNS configuration.
This is an excellent way of working with a standard project that you base other projects on. Having set it all up, you can simply spawn a duplicate at will and implement any changes.
Maintains the Git history of the source project. This allows you for example to merge back the new changes into the source project.
Transfer allows you to move your project from one organisation to another. Please mind that there are limitations when your project has a live server. To mitigate downtime a transfer needs to be initiated through Divio support.