It would be nice if the name reflected the SI's concern that the dangers come not just from some cunning killer robots escaping a secret government lab or a Skynet gone amok, or a Frankenstein monster constructed by a mad scientist, but from recursive self-improvement ("intelligence explosion") of an initially innocuous and not-very smart contraption.

I am also not sure whether the qualifier "artificial" conveys the right impression, as the dangers might come from an augmented human brain suddenly developing the capacity for recursive self-improvement, or from some other creation that does not look like a collection of silicon gates.

If I understand it correctly, SI wants to ensure "safe recursive self-improvement" of an intelligence of any kind, "safe" for the rest of the (human?) intelligences existing at that time, though not necessarily for the self-improver itself.

Of course, a name like "Society For Safe Recursive Self-Improvement" is both unwieldy and unclear to an outsider. (And the acronym sounds like parseltongue.) Maybe there is a way to phrase it better.