Does LogoVerify register or file my trademark?

No. LogoVerify checks a name and a logo before you use them or file; it does not file applications, register trademarks or act as your attorney. When you are ready, you file at the USPTO yourself (on the USPTO website) or through a trademark attorney or a filing service, and your LogoVerify report shows what an examiner is likely to weigh. (General information, not legal advice.)