To change the name of the application, you can select the new target, click the Build Settings tab, look for the Packaging section and change the Product Name. You'll notice the entry in the Products group in the navigator changes.
Since Xcode automatically creates matching schemes for each target by default, you'll also need to make sure the scheme for your new target is set to build and launch the new target's matching executable. To do this, select the scheme from the popup then choose edit scheme from the same popup. Select the Run action in the scheme editor sheet and make sure the Executable popup is set to your new target's newly-renamed executable. Do the same for the Profile action so it does the right thing when using Instruments and all. It should be properly selected already, but sometimes Xcode gets confused when renaming/moving things around.
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