I would add that the casual and wide use of the STEM acronym to mean often very different things has contributed to a sense of confusion and scatteredness in this domain.  The question of "What is STEM?" was addressed by the National Academies in a recent report (http://www.nap.edu/catalog/18612/stem-integration-in-k-12-education-status-prospects-and-an)  that looked at how and to what effect the four STEM disciplines are connected in K-12 education.

I believe the only rule on state-identified STEM centers is the first one to claim it gets the name.  However, there are a few multistate groups which link such organizations, including STEMx at Battelle in Columbus, OH, and the Midwest STEM Consortium run by Prof. Jeff Weld at Northern Iowa.  Between these two organizations about 30 state groups are identified and linked.  Additionally, each state is likely tied to states outside of these groups, enhancing communications a bit more.  I don't know of any standard rules for claiming names or determining the scope of work in each state, and almost every state is different from the others in structure and function.  There are no national standards or even recommendations that I have ever seen.  Indiana and a few other states have adopted strict standards on which public schools can call themselves "STEM schools" which helps reduce confusion for K-12 at least.  Additionally, the Indiana Afterschool Network has standards and assessments for out-of-school STEM programs to bring more rigor to those providers.