When you are to make an information model for the business operations of an organization (in your case, a public library), you have to identify all entity types involved (e.g., users, media types, media items such as books and DVDs, loans, reservations, etc.) and the associations between them (e.g., the class User would be associated with Loan).
But you don't include a class for the organization itself (or its information system) in the model. Consequently, do not include a class for "loan service".
This approach results in an information design model that is the basis for deriving both an OOP class model for defining model classes (also called entity classes) and a database table model (e.g., for defining a MySQL database schema).
The model/entity classes provide the foundation for your app or IS.
Depending on your app development approach (e.g., the chosen framework), you may have to design other classes (e.g., for the user interface), but, compared to the model/entity classes, they are less fundamental.
