"Identifying Objects in the problem/business domain" is a requirements analysis task, which should not be confused with detailed class design. It is one way to use classes as a rough ordering tool for "user stories" or requirements, but they should not be the final classes one wants to create during design and implementation (at least not if one prefers to get some maintainable piece of software).

The classes in code, however, should be the ones following the SRP, thus will be much more fine-grained than the classes one uses during requirements analysis and typically on a different level of abstraction.

"Identifying Objects in the problem/business domain" is a requirements analysis task, which should not be confused with detailed, technical class design. It is one way to use classes as a rough ordering tool for "user stories" or requirements, but they should not be the final classes one wants to create during design and implementation (at least not if one prefers to get some maintainable piece of software).

The classes implemented in real code, however, should follow the SRP. They will be more fine-grained than the classes one uses during requirements analysis and typically on a different level of abstraction.