I had assumed the question was more aimed towards LessWrong, not serious academic usage. I'd expect academic references to be in the form "I work for MIRI", not cutesy shorthand.
Still, no one walks around calling themself a CSAILian. If there are people calling themselves Mirians, even if those people aren't directly affiliated with MIRI, that could hurt MIRI's credibility, I suspect, because it would make them seem unusual relative to other serious research groups.
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.