Every organization must assign someone as the officer responsible for maintaining a bully-free environment. For larger companies it is typically the responsibility of the Human Resources department. In smaller companies, it can be the CEO/Owner or someone assigned by him/her.
However, the person responsible must have a thorough understanding of how bullying and harassment can impact the employees. He or she must also understand that there can be serious consequences for the organization if incidents of bullying and harassment are not addressed adequately. That is why it is important for the responsible person to go through some appropriate training on this issue so he or she can be successful in performing this task. I have experience with a Human Resources Director who was not very proficient in handling issues of this nature.
The main point is that the person must be able to put in appropriate processes and procedures to be able to handle any complaints from employees and then follow through rigorously in a timely manner. It is important for employees to develop a trust that any complaints will be taken seriously and appropriate investigations will be conducted according to the established processes. It is not good for the companies if the employees feel that no one cares about these issues and if they believe that they will face some form of retaliation if they made a complaint.