While you can rename your directory as the others pointed out, keep in mind that doing so will take your old site down immediately.
I’m not too familiar with the shell, but you should be able to use the cp command to copy the files once logged in.
If you don’t mind taking your other site down, by all means rename the folder. You may want to set up redirection immediately though. If you have any concern that paths may be an issue, I would copy it instead of renaming it and debug any issues before taking your old site down.
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