For one, I'd strongly suggest updating to the latest Android Studio (0.3.7 as of now); there are tons of bug fixes.
You're running into bug https://code.google.com/p/android/issues/detail?id=57692, which is that if you try to use the UI to rename modules or your project, it doesn't update the build files. Sorry, it's really broken right now. I'd suggest changing the directory names directly in the filesystem, and updating your settings.gradle file to reflect the changes. Your project on disk should look something like this (with many more files than what's shown here):
projectFolder
|--settings.gradle
|--applicationModuleFolder
| |--build.gradle
| |--src
it uses projectFolder's name as the project name and applicationModuleFolder as the name of the module that your Android App lives in (the upper and lower outlined boxes in your screenshot, respectively). I think the way your project is set up now, they both have the same name; you can rename both to the same new name if you like, or you can give them different names; it doesn't matter.
Once they're renamed, edit your settings.gradle file; it will look something like:
include ':applicationModuleFolder'
just change the name to your new name there as well. Once these changes are made, click the Sync Project with Gradle Files button in the toolbar (if you're running a very old version of Android Studio, it may not have that button, so you can close the project and reopen it in that case) and it should pick up the changes.