Often, yes. When a truck driver causes a crash while working for a motor carrier, the company can generally be held responsible for that conduct — the same way a business is accountable for the people it puts on the road on its behalf.
Beyond responsibility for the driver, the company can be directly at fault for its own choices: hiring a driver with a dangerous record, failing to train or supervise, pushing schedules that encourage fatigue, or neglecting maintenance. These are separate claims that can apply even when the driver is also at fault.
Reaching the company matters because it usually means deeper insurance and often reflects the real cause of the crash — a decision made in an office, not just a moment on the road. Establishing it typically requires the company's internal records, which is another reason to act early.