New York State would be quite a brand name. It is hard to believe that "Alaska State" or "Wyoming State" would have quite the carriage.
The problem is that the name is
too elite and
too good. Many other schools in New York would want it. The name is so good that schools in
other states would want it (lol).
If there had been a developed New York State 50 years ago, the Big Ten would have probably taken it with PSU and gone to 12, with another "N"- as in Nebraska- a footnote in history. The New York system seems to put more emphasis on academics vs. athletics. A major state athletic flagship has always been
well within the resources of the great state of New York (I am from Ohio, BTW).