Answer: Yes. You only have to take care to not define Senior Management as the responsible role in too much activities.
2 - If so, do I have to specify who is meant by Senior Management?
Answer: Yes. Instead of concepts like manager or process owner, Senior Management may mean one or more persons, like when you define the responsibility to project team. In these cases people, and auditors usually look for the one in the highest position, so you should make well clear what Senior Management means to your organization.
3 - If so, where do I have to do this? In which document?
Answer: You have many options where to define the Senior management. You can define them in job descriptions, in the organizational chart, or in the Information Security Policy.