I have stumbled this issue a couple times. It used to be a complicated thing actually.

In Xcode 5.1.1, you can do it by simply renaming your Target. Double-click on the Target name to change it.

Previously:

• Select your target under the Targets section.
• Go to the Build Settings tab.
• Scroll down to Packaging.
• Change the Product Name to the desired one.

That is because Agreed. Bundle ID points to PRODUCT_NAME. PRODUCT_NAME points to TARGET_NAME. So changing the target name will propagate to the bundle ID. Until I read this I was expecting to see the target name as a property of the Target; wasn't thinking of clicking the target itself to change its name.