iOS Rename app Target

I've started working on an app and I would like to have a paid for version and a LITE version. In my fresh new project I duplicated the original target for my app. I then changed its name from MyAppcopy to MyApp Lite. I also renamed the resulting info.plist. But in the drop down menu where I select the active target it still shows it being named as MyAppcopy and when I run it on my phone the name shows up as MyAppcopy. I would like it to show MyApp Lite, the actual name of the target I'm using.

Edit: I tried changing the product name. This solved the issue of the naming on my phone, but the drop down is still named wrong.

Thanks, worked perfectly!