That depends. If you have run a successful project on Kickstarter, your account name will be locked. You will not be able to change it for use on Drip.
If you do not have a successful project attached to your Kickstarter account, you will be able to change your profile name on Drip. Just visit your profile settings on Kickstarter and update your name there. (The change will apply to both Kickstarter and Drip.)