You can register a logo with the USPTO by using the Trademark Electronic Application System (TEAS) or other online trademark service. If your logo includes design elements, you will need to upload an image, using a . jpg file, of the logo as part of your trademark application.
Although you can apply for trademark protection for your name and logo concurrently, each is considered a separate mark. As such, each mark (i.e. your standard character mark and your design mark) requires its own application.