My impression is that anyone who has ever heard of Singularity University doesn't even have it in their hypothesis space that you mean something different when you say Singularity Institute.
Yup.
Even when they do have it in their hypothesis space, it still gets mangled. I recently got a follow-up email from someone that still thought I was Singularity University. I had briefly explained to him about how SU had acquired the Singularity Summit from us, and his follow-up email said "now that you have acquired the Singularity Summit, you may be interested in my product..."
http://singularity.org/blog/2013/01/30/we-are-now-the-machine-intelligence-research-institute-miri/
As Risto Saarelma pointed out on IRC, "Volcano Lair Doom Institute" would have been cooler, but this is pretty good too. As the word "Singularity" has pretty much lost its meaning, it's better to have a name that doesn't give a new person all kinds of weird initial associations as their first impression. And "Machine Intelligence Research Institute" is appropriately descriptive while still being general enough.