Liechtenstein is a first-to-file jurisdiction, which means you generally only obtain trademark rights by registering your mark. Only in exceptional cases can an unregistered trademark be protected.
To secure protection, you must file an application with the Bureau of Intellectual Property of the Office of Economic Affairs (LIPO) in Liechtenstein. You can also seek protection via an international registration through the Madrid System, designating Liechtenstein in your international application.
If you file a combined mark (word + logo), your exclusive right is limited to the exact configuration registered. If you plan to use and protect the word element and the logo separately, you should file additional applications for each version.