- Create the new bucket with the desired name.
- Go to the old bucket and select all files: click the first and then shift+click the last.
- Above the file listing, in the button row, is one marked "Actions", which opens a menu that includes "Cut" and "Copy". Pick one.
- Go to the new bucket, click Actions, and Paste your files.
Why would anyone want to rename a bucket? In our case, we created a StudlyCapsStyle bucket, which can't be used with CloudFront's dns-compatible-style.
In double-checking this post for accuracy, I noticed that Cut/Copy are available on the right-click menu for a single selection, but not the multi-select. Weird.