Change it in the build tab of the targets settings page
As clarification: select targets, select the target you are building, get info, select the build tab, write 'product name' in the search box, and change it there.
OK, here is what I found, took me a bit of hunting after reading this post, so hopefully this answer will help everyone:
1.In the project contents pane at left, click the Folder icon.
2.Select the top-level blue line representing the project.
3.If you don't have the Inspector pane (right pane) open, click the button to enable it. This is the third button in the "View" toolbar towards the upper right corner.
4.In the Inspector pane, click the little folded-corner paper (file properties) icon.
5.First thing is Project Name. Type in a new one, you will be prompted to rename project content files.
I should add, this will leave your old app with the original name in the simulator, so you still need to delete it from the simulator. Also any files you created in the old app bundle will not be brought forward to the new bundle (unless you find them in Finder and move them over).
(EDIT:) One more important note. Renaming your bundle will mean that the App Bundle Identifier you registered with Apple Provisioning Portal will no longer work for that app. You will need to generate a new App ID and Provisioning Profile in order to distribute your app to a physical device.
One thing that seemed to help when I went through this is in Xcode 4 is that it appeared to be necessary to delete all the schemes. Prior to this it seemed that although the app would be compiled under its new name, it'd be as the old name in the simulator. However, I did do other desperate measures like re-start xcode and delete the app out of the simulator folder so it's hard to be certain that deleting the schemes was the key.
In Xcode 4, select your target, "Info" tab, and set the "Bundle display name" field to the name you want (i.e. "MySuperApp"). This is the simplest, pain-free solution.
All other answers described here do not address the original posted issue: "I want to change the name which is displayed below the app icon on the iPhone screen." The upvoted answers of: Woody, Jay, and youshunei are OK but they will all change the displayed name AND either:
A) change your App Bundle Identifier and cause an incompatibility between your app and the Bundle Identifier you registered with the Apple Provisioning Portal (which is a problem if you have already distributed your app or intend to submit the app)
OR
B) result in scheme issues that others have mentioned (i.e. needing to delete/re-create existing schemes)
You want to change the Bundle Display Name in your project.plist.
Bundle display name : ${PRODUCT_NAME}
should be changed to
Bundle display name : MySuperApp
This changes the label of the icon in iOS without actually changing the app identifiers.
If you just change the bundle display name, you won't need to set up a new app id and provisioning profiles.
Making the product name change:
Double click the name right under "Targets" and modify the target name to whatever you want.
Checking if the change has been made:
Click on "Target" and on the right hand side search for "Product Name" under "Build Settings". The displayed value of the product name should reflect your change. If not, double click on that name to make sure it's being set to $(TARGET_NAME).
In recent versions of XCode (I am on 4.3.2 currently), $(PRODUCT_NAME) is set to $(TARGET_NAME) which defaults to the name of the project directory (no don't change the directory name).
Solution: Click on the file navigator. Click on your blue project icon. Look for the TARGETS list (under the PROJECT list). Hover-click your target; then rename it to your product name.
Aside: If you are having code-signing problems, I found that deleting, revoking, and regenerating all certificates/keys, and profiles fixed my problem. I tried everything else first!
The issue I was having was that I have multiple Info.plist files in my Xcode project. In order to ensure I had the right one which contains the Product Name, I moved the existing Info.plist temporarily to force Xcode to allow me to choose another one. Since Info.plist is not part of a target, but part of the Project configuration, this was the only way I could find to do this.
Select Target and single click to edit and rename and you're done
You can see the product name gets changed
Here the snap for these 3 steps
Edited:
I've noticed the similar answer with image attachment by youshunei after my post. So, I would add a bit more information here that I've tested it on Xcode 6.3.2 and it doesn't need any restart.
Edited:
When I renamed one of my Mac OS X app which contains comma in its name the same way. I got missing file (name trimmed up-to comma) in some pod linking library. So, I have to rename my app at Target -> Build Settings -> Product Name