DL44
Once your DL329S form is filled out, you'll need to fill out an application for a new Driver's License or ID Card. The DMV no longer provides paper applications, so you'll need fill out your application online using form eDL44, or on a computer at the DMV.
When the application asks you what you want to do, select "Correct or update my driver's license or ID card", and then select whether you have a driver's license or an ID card.
When asked for your full legal name, enter your new (changed) name. When asked for any previous names, enter your previous (unchanged) name.
Once you fill out your online form, a confirmation email will be sent to you with a code. Take that code to any DMV field office to complete your application.