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Get the full path of your stack something like "Leonardo/myproject/mystack" and call

pulumi stack rename Leonardo/newproject/mystack

then update the Pulumi.yaml to match.

thank you @echoing-dinner-19531 though that renames the stack, I want to rename the project

If you give the fully qualified stack path but only change the project part it will rename the project.

thank you @echoing-dinner-19531 trying...