How to change an Android app's name?

Yes you can. By changing the android:label field in your application node in AndroidManifest.xml.

Note: If you have added a Splash Screen and added

<intent-filter>
            <action android:name="android.intent.action.MAIN" />
            <category android:name="android.intent.category.LAUNCHER" />
</intent-filter>

to your Splash Screen, then the Launcher Icon name will be changed to the name of your Splash Screen Class name.

Please make sure that you change label:

android:label="@string/title_activity_splash_screen"

in your Splash Screen activity in your strings.xml file. It can be found in Res -> Values -> strings.xml

See more here.

There's the android:label for the application, and the android:label for the launch activity. The former is what you see under Settings -> Applications -> Manage Applications on your device. The latter is what you see under Applications, and by extension in any shortcut to your application, e.g.

<application
    android:label="@string/turns_up_in_manage_apps" >
    <activity
        android:name=".MainActivity"
        android:label="@string/turns_up_in_shortcuts" >
        ...
    </activity>
</application>

This is a simple thing in Android Studio,

go to: res folder -> values -> strings.xml

change the app_name (in the bellow example:MitsuhoSdn Bhd) to any new name you want.

<string name="app_name">MitsuhoSdn Bhd</string>
<string name="hello_world">Hello world!</string>
<string name="menu_settings">Settings</string>