I would like to call this proposed institute (separate from ExI) something along the lines of the "Institute of Future Sciences" a quick web search revealed a New Age <something> with the same name, whether it's real or not is hard to tell. IMHO, the name should embody the idea without refering to transhumanism or extropianism directly.
Goals: Educate the public to the potential of future developments in science and technology in a clear and rational manner. Establish the means for the academic pursuit of new and emerging science and technology. Or in other words, bombard the media with critical evaluations of future developments in science and technology in a hope to over come the inherent "disasterbation" and spread the tranhumanist meme. And try to organise transhuman-oriented courses at all levels of academia and encourage the publication of transhuman-oriented papers.