I think a name change is a great idea. I can certainly imagine someone being reluctant to associate their name with the "Singularity" idea even if they support what SIAI actually does. I think if I was a famous researcher/donor, I would be a bit reluctant to be strongly associated with the Singularity meme in its current degraded form. Yes, there are some high-status people who know better, but there are many more who don't.

Here is a suggestion: Center for Emerging Technology Safety. This name affiliates with the high-status term "emerging technology", while terms with "Singularity" and even "AI" often (unfairly, in my opinion) strike people as being crackpot/kooky. Admittedly, this is less descriptive than some other possible names (but more descriptive than "The I.J. Good Institute"), but descriptiveness isn't the most important factor. Rather, you should consider what kind of organization potential donors or (high-status) employees would like to brag about to the their non-LW reading friends/family at dinner parties.