I'm not sure about including "Machine Ethics"; given that there already is such a field, and given that (AFAICT) it does not generally involve precision-grade philosophy suitable for (let alone intended for) the construction of a Benevolent Really Powerful Optimization Process, it may be misleading to appropriate that name.

Hard to say. I feel like the Friendliness question is a natural fit for the field- in fact it seems plausible to me that it is the machine ethics equivalent of unified field theory. You're right, though that the field mostly deals with minor, less rigorous issues. I don't know- my criterion for the name issue is basically "Could I tell family and friends I was working at a place with this name without being laughed at or getting strange looks."

I do like the suggestion to use "Center for...", though "Institute" doesn't necessarily sound like a connection to academia is being implied (at least to me — do you think this is incorrect?).

Not strictly speaking, no. Center is less pretentious, though.

Center for Technology and Existential Risk?