Earlier quoted context omitted.
It's also worth noting it's not the hospital itself actually objecting to anything, it's the San Francisco City Council. I'm not sure they actually have any power over it one way or the other.
I wonder if the hospital should release a statement supporting Zuckerberg and the donation? Politics in San Francisco are out of control. In my estimation from afar it's like the liberal version of the colloquial Alabama conservative politics.
Let's start by assuming that the city has a reason for their stance; as I assume you do for thinking that politics in the city is out of control.
Providing donations for healthcare services is admirable, and I don't see any issue with Zuckerberg doing that with his name attached.
Requiring your own name to appear on everything from street signs to labcoats for fifty years as part of the conditions of the donation, however, seems unusual at the least.
People with all kinds of intentions will try to create outrage from situations like this. I think it's worthwhile to be curious and learn and discuss the details. It'll probably all become clearer with time if you talk to people rather than antagonize them.