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I would disagree with whole ""how it is seen by the world"" statement.  First of all, it will be seen by the world as it presents itself.  I really doubt after they stop using SUNY at Stony Brook, which they just have, that this name will last in anyones memory for long.  I would also point you to some less political references than those you put up, such as the wikipedia article for University at Buffalo, State University of New York.  They did the same thing a while back, and their website uses that designation.  Berkely is the same way.  It is technically UC Berkeley, but that isn't what you see on their website.

It would not be surprising that anything from SUNY head office or whatever it is would continue to use the old designation, but that is politics, and is hardly an area we need to play to here.  If they could stop Stony Brook from changing their name, they would.  No bureaucrat gives up power if they can prevent it.  It is a fait accompli.

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