What is the name of the hospital in Grey's Anatomy before the merger?

Before the merger, the hospital in Grey's Anatomy was called Seattle Grace Hospital.

It is the fictional Seattle hospital where Meredith Grey begins her surgical internship alongside Cristina Yang, Izzie Stevens, Alex Karev, and George O'Malley. Richard Webber serves as chief of surgery, while Derek Shepherd leads neurosurgery and becomes one of the hospital's most prominent surgeons.

During Season 6, Seattle Grace merges with Mercy West Hospital. The combined institution is renamed Seattle Grace Mercy West, bringing new residents such as April Kepner and Jackson Avery into the existing staff and creating intense competition for jobs and surgical opportunities.

The name Seattle Grace Hospital is therefore the correct pre-merger answer. It should not be confused with Grey Sloan Memorial Hospital, the later name adopted in Season 9 after the doctors purchase the hospital and rename it in memory of Lexie Grey and Mark Sloan.