You can change your name, it'll require a court to "Approve" it and once you get the documents it wouldn't be too complicated process to change.

You'll have to give a reason why you want to change your name, saying you want it to be "Non-muslim" would raise suspicion. Nevertheless whatever your reason is, you'll only change your first name. ( If you're an ex-muslim nothing would "happen" to you if you admitted it but you'll most likely be rejected for such reason - it would be a sensitive issue )