Yes, it really was renamed after the Zuckerbergs, as buildings sometimes are at the request of a large donator seeking posterity.

See Wikipedia:

In November 2008, San Francisco voters approved an $887.4 million general obligation bond for the General Hospital rebuild, work began in 2009, and was expected to be finished in 2015.

In 2015, Facebook founder and CEO, Mark Zuckerberg, and his wife Priscilla Chan gave $75 million to help fund equipment and technology for the new hospital.