To change your application name , you need to change it for Android and IOS :
You can use rename package to make it easy .
Just run this command inside your flutter project root
pub global run rename --appname "My application"
or
Edit AndroidManifest.xml for Android and info.plist for iOS
For Android, edit only android:label value in the application tag in file AndroidManifest.xml located in the folder: android/app/src/main
Code:
<manifest xmlns:android="http://schemas.android.com/apk/res/android"> <application android:name="io.flutter.app.FlutterApplication" android:label="Your Application Name" //here android:icon="@mipmap/ic_launcher"> <activity> <!-- --> </activity> </application> </manifest>
Screenshot:

For iOS, edit only the value inside the String tag in file Info.plist located in the folder ios/Runner .
Code:
<plist version="1.0"> <dict> <key>CFBundleName</key> <string>Your Application Name </string> //here </dict> </plist>
Screenshot:

Do a flutter clean and restart your application if you have a problem.