What is the name of the hospital after the merger in season 9?

The hospital after the Season 9 merger is Grey Sloan Memorial Hospital.

The name was adopted after the doctors involved in the plane-crash lawsuit used their compensation money, with help from the Harper Avery Foundation, to purchase Seattle Grace Mercy West. They renamed the hospital to honor Lexie Grey and Mark Sloan, who died as a result of the crash and its injuries.

The hospital had previously undergone several name changes. It began as Seattle Grace Hospital, merged with Mercy West Hospital during Season 6, and became Seattle Grace Mercy West. The Season 8 plane crash and its legal aftermath ultimately led to the Season 9 renaming.

A common mix-up is confusing the merger with the renaming: the merger created Seattle Grace Mercy West, while Grey Sloan Memorial Hospital came later, after the survivors purchased the financially troubled institution.