What is the cleanest way to rename a running stack so the next pulumi up does not confuse pulumi?

What are you trying to accomplish?

Definitely need to know what problem you are trying to solve since renaming a stack is not a common practice in my experience. As long as

getStack()

is not used in a resource's name, you might not have any issues.

Set up a stack that was dedicated to a single purpose named “one-thing” now I have decided that the stack name was stupid and should be called “other-thing”. “one-thing” is in prod now. Its as simple as that.

Have you looked at

pulumi stack rename

command? It should provide what you need.