There are a lot of positive and negative opinions being thrown about by various fans and on both sides there are some legitimate points people need to consider.
In Favor of the Branding
Fully 70% of UB Students are not from Western New York and the largest single contigeny of students on campus are from, you guessed it, Down State. When you add up non Western New York fans who still live in NY you get to about 50-55% of the student body versus 29% or so for Buffalo.
Names Matte! There is a reason OSU is known as "The Ohio State University" and not just Ohio State University. They tried the latter but were blocked by our conference mates in Athens who clung to the name. There have been other fights around names, typically having your institution known as "STATE UNIVERSITY" is a big marketing plus.
As it stands *today* UB has the strongest athletic claim the the name "New York State" among the State University centers. Institutionally the only school who is close in terms of size and endowment is Stony Brook. They are close to UB in size, they are AAU, and the two are academically comparable. What they don't have is membership in an FBS conference.
So do you want to try and have the Athletics flagship for New York in your back yard or not?
Opposed to the Branding
UB has been a Buffalo institution for 160+ years. It was founded at the corner of Baily and Main and grew with the city until it joined the SUNY. They have been playing sports under the name Buffalo for 100 years and many alumni might not like New York being played up over Buffalo.
Moving away from the brand "Buffalo" might potential alienate Buffalo sports fans who are otherwise unaffiliated with the University.
On the floor
I am ok with "New York" being bigger than Buffalo but could we have maybe made the "Buffalo" component just a tad bigger. As it is it looks like it was only put there because you "had to".