No, the employer is not entitled to know your diagnosis but it is entitled to receive sufficient information to address the situation properly. Only the information necessary for determining the appropriate form of accommodation has to be shared.
As an employee, you are responsible for ensuring that your employer gets the list of functional limitations your treating physician has set out, having regard to your existing job requirements.
It is therefore a good idea to share your existing job description with your doctor so that he or she can appreciate the scope and nature of the work that you do and properly advise the employer of your functional limitations. Your doctor should also indicate how long such functional limitations are expected to exist. This will provide an estimate of how long the accommodation may be required by the employer.
This kind of information is not usually required for employees who have readily evident disabilities such as permanent physical disabilities for instance.