Nope. When you see the step to login with Facebook, just click the link that says, "I don't have a Facebook account" if you'd rather not use Facebook. If you choose to give this way, your donation will appear anonymously.
Benefits of logging in with Facebook: We recommend that you log in with Facebook because we can keep track of your gift card for you. You will never have to re-enter your card number, and we can send you a verification of your donation. You will also be able to share your donation with friends, showing them what you care about, and attach the donation to your Causes profile. This is all for your benefit and we respect your privacy.