Hiding your signature from public view is easy! Simply go to your Change.org account and visit your User Profile page. Hover your mouse over a petition you wish to hide and you'll see an X button pop up. Simply click that and it will be hidden from your profile.
Please note that this does not mean that you will be able to unsign a petition, nor can any signature emails that have already been sent to the target be unsent. This will, however, prevent anyone who finds your public profile on the web to see what petitions you have signed.