UPDATE: From the comments this answer seems to be out of date
The Flutter documentation points out where you can change the display name of your application for both Android and iOS. This may be what you are looking for:
It seems you have already found this in the
AndroidManifest.xml as the
Review the default App Manifest file AndroidManifest.xml located in
/android/app/src/main/ and verify the values are correct,
application: Edit the android:label in the application tag to reflect the final name of the
Review Xcode project settings section:
Navigate to your target’s settings in Xcode:
In Xcode, open Runner.xcworkspace in your app’s ios folder.
To view your app’s settings, select the Runner project in the Xcode project
navigator. Then, in the main view sidebar, select the Runner target.
Select the General tab. Next, you’ll verify the most important
Display Name: the name of the app to be displayed on the home screen