how could I add a logo to this video in order to protect my copyright?

Hi, I'm guessing that you mean 'watermarking' your video. If that is what you're trying to do you can build one in Photoshop and add it as a layer in your Premiere timeline. If you use the Photoshop option make sure that you use a transparent canvas and make your logo or typeface 40 to 50 percent transparent (experiment with transparency to determine what looks best for your design). Once you've created your title you can import it into Premiere. You can also use the titling feature in Premiere and create or import an existing logo and position and add transparency (all of this can be done directly in Premiere without using Photoshop).
You will get the best quality watermark if you add it with your encoding program (not in Premiere) such as Sorenson Squeeze. Squeeze has a import and add watermark function. This will give pristine results for the graphical element.

As an aside if you've created a video and made a copy of it, it's automatically considered as a work that is copyrighted. It's a good practice to add a simple copyright (see sample below) at the end of your video. If you've got a masterpiece that you really want to go the extra mile to protect you can register it with the Copyright Office at the Library of Congress.