AI Impacts Research seems to me the best of the bunch, because it's pretty easy to understand. People who know nothing about Eliezer's work can see it and think, "Oh, duh AI will have an impact, it's worth thinking about that." On the other hand:

• Center for AI Safety: not bad, but people who don't know Eliezer's work might wonder why we need it (same thing with a name involving "risk")
• The I.J. Good Institute: Sounds pretigious, but gives no information to someone who doesn't know who I.J. Good is.
• Beneficial Architectures Research: meaningless to 99% of the population, agree with whoever said people will think it's about bridge design.

Somehow, "AI Impact Research" sounds better than "Impact," perhaps to avoid the "reads as a sentence" thing, or just because my brain thinks of "impact" as one (possibly very complex) thing. Also agree that "society" or "institute" could go in there somewhere.