You should analyze not the classes you will create in your program, but what classes will handle, remembering that objects are different from classes:
- An object needs a class to exist;
- A Class does not require an object to exist;
A known definition is: "An object is a term we use to represent a real-world entity."
Objects should be in your diagram, as they will have their attributes and will be manipulated according to your need for business rules.
Following the line of thought quoted by you in the question, a system that has Customer and customerCatalog, Official and employeeCount, will have as entities the Client and the Employee, as they are the entities of the "real world."
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