The idea of "branding" covers a lot of ground these days but for the moment think of branding as visually linking your professional materials together so that your name, title and contact info are presented the same way on all your materials. This visual identity can be created with "type treatments," logos, and perhaps, images. The trick to creating an effective visual identity that will brand your materials is 1) finding a look and feel that's in synch with the work in your portfolio and 2) using it consistently. That can be as simple or as complicated as you want to make it.
TYPE TREATMENT: Create a type treatment for your name by finding several fonts that you like- nothing too off-the-wall. Try out each font with your name and title (P.A., Actor, Designer, Writer, etc) if you choose to use a title. Then try them out at different sizes and in different colors. Print them out so you can see what they look like on paper.
LIVE WITH IT: Tape your type treatments to the wall or the fridge and keep an eye on them for a few weeks. Some designs will begin to look crappy after a while and can be eliminated. Eventually one will emerge as superior. Then find a second font that is perhaps a plainer version of your "brand" font to use for your contact information.
LOGOS: The ideal logo is unique and totally synced up with your artistic (or whatever) sensibility. But frankly, creating a great logo for oneself is a daunting task. Most students haven't clearly defined their artistic sensibilities nor do they have the advanced design skills that are essential to the task. Graphic designers, on the other hand, are trained to create intuitive and striking visual identities. If a simple and professional-looking type treatment of your own design doesn't do it for you, get a designer. (Before beginning work on a logo with a designer, be ready to articulate who you are as an artist, what your ideas are for the logo, and have examples that will help the designer know where to begin).
BRAND IT: Brand all your materials together by using your type treatment/logo on your website, print book, DVD cover, business cards and all materials that will represent your professional life. Your type treatment or logo should be sized up or down to fit your different pieces. A basic branding strategy will add a consistent visual identity to all your professional materials- that is recognizably yours.
CAUTIONS: 1) Print small quantities. Things change. 2) It's easy to create a goofy looking logo. Don't. 3) People have been trying to devise interesting logos from their initials since the alphabet was invented. No one has succeeded.