Whether you're going to call it a process or an activity or whatever it's up to you. To address risks and opportunities just take into your account:
1- The size of your organization and its context,
2- The complexity of your processes,
3- The competencies of the people who’re doing the job.
Risk identification and treatment are two sub-processes of any typical risk management process. If you're working in a small business, just filling a risk registrar after a brain storming session about associated risks to your company might be helpful.
On the other hand, if you're working in a medium or large corporation, a detailed risk management process should be implemented, a certain budget will be needed, risk workshop will be held, etc.
I hope this is helpful to your question.
Mohammad Elshahat