Changing the name of the file will do nothing. When the app is installed, it'll still have the same name (file name of the APK doesn't matter at all).
EDIT: As for how to do this, use apktool to unpack the app. Open "AndroidManifest.xml" and look for something like the following (in this example, I am using a manifest from Canabalt):
Code:
<application [COLOR="Red"]android:label="@string/app_name"[/COLOR] android:icon="@drawable/icon" android:name=".CanabaltApplication" android:debuggable="false">
The important one is the red one. Sometimes it will say something like android:label="Canabalt HD", in which case you'd just change it to what you want, and then rebuild it with apktool, but in this case there is an @ at the start of the name, which means that the name is stored in another file. As it is "@string/app_name", this means that the name is stored in the file "res\values\strings.xml" and has the name "app_name", so go into the folder "res", and then within that the folder "values" [if you use another language on your phone than the app's default language, go into the relevant folder e.g. for Spanish, you would go into "values-es" instead] and then within that open the file "strings.xml". Then you would look for something like this:
Code:
<string name="app_name">Canabalt HD</string>
Change this, save the file and then rebuild the APK with apktool. Afterwards, you'll need to sign the APK. Otherwise, it MAY be possible to take your edited APK, open it with 7zip, extract the file "AndroidManifest.xml" (or whatever file you edited e.g. strings.xml), then open the original APK with 7zip and replace the AndroidManifest.xml (or whatever file) with the modified version, and then not have to sign it. I haven't tried this though.
Also note that if there is an @ in the AndroidManifest.xml, you can still just edit the title in that file without finding the relevant entry in another file. In my above example, if I wanted to change the name to "Canabalt MOD", I'd change it to the following:
Code:
<application [COLOR="Red"]android:label="Canabalt MOD"[/COLOR] android:icon="@drawable/icon" android:name=".CanabaltApplication" android:debuggable="false">
The difference is basically doing it this way, it won't change for other languages, it will ALWAYS be "Canabalt MOD", regardless of the language of the phone. If you're just doing this for yourself, that probably doesn't matter, so it's simpler to just change it in AndroidManifest.xml.