Center for Machine Ethics (or Institute for...)
Institute for Reducing Existential Risk
Center for the Reduction of Existential Risk
"Machine ethics" is, as far as I can tell, the actual name in the literature (insofar as there is any). I also really like how it sounds. The general "Reducing existential risk" angle probably requires the organization to get broader in it's focus and focus on other risks (or else be seen as deceptive). But that might not be a bad thing and it may be the way to getting a lot more money and being seen as a mainstream charity.
Also I'm not sure how sold I am on "Institute" it's got a 'we're pretending we're associated with academia' feel to it. I think "Center for..." sounds a lot better.
"Machine ethics" is, as far as I can tell, the actual name in the literature
"Machine morality" has better alliteration.
If you have graphic design experience, check out the on-going logo design competition at 99designs for the Singularity Institute. There are still 6 days left to enter and be eligible to win the $295 prize if your design is selected. Tell your friends with graphic design experience too. There are very few submissions currently.
Note: This is a blind contest. Designers can only see their own entries. All designs will be revealed when the contest ends.
If you're interested at getting a peek at the designs, they will be online after the competition is over. This is standard practice in 99designs contests to prevent designers from contaminating each other and having all the designs drift in a certain direction.