Is it reasonable for the company to let us file a lawsuit against the perpetrators of intentional injury on the construction site in our own name? What do we do? What's the procedure?

If the nature of the case has been identified as a criminal case by the public security organ, the procuratorate will initiate a public prosecution, so is the person who hit you intentionally hurting or intentionally killing? In the process of criminal trial, you file an incidental civil lawsuit in your own name, and at the same time sue the person who hit you and your company for compensation. If it is a simple civil case, you should sue the hitter and your company yourself and ask them to share the responsibility.