Rhetoric check: arena now dubbed "Barclays Center of Brooklyn," taking advantage of Brooklyn connection (and connoting civic virtue)
What's in the name?
Clearly arena promoters are taking advantage of the geographic location--Brooklyn's got a lot of buzz these days--but there's something more going on, I'd suggest.
It's very unusual to attach a geographic location to an arena, as these lists of United States and Canadian arenas show. (Ditto for stadiums.)
Of the few arenas with geographical locations, it's not typical to use "of." The list includes, for example, HP Pavilion at San Jose.
What it means
The name "Barclays Center of Brooklyn" is designed, I believe, to leave the impression that the arena is somehow embedded in the borough, a contributor to civic virtue and local coffers.
Actually, private profits will flow to arena operators (under the fig leaf of public ownership, devised to allow tax-exempt bonds). The arena won't be operated in the public interest.
It's not being "presented" to Brooklyn, as Barclays promised in 2007 (see advertisement at right), after buying naming rights.
It's another somewhat deceptive use of a name, not unlike the way "Atlantic Yards," the name of a project, suggested that the project would be limited to the railyards--which represent less than 40% of the site.
(See Rhetoric check: the use and misuse of "Atlantic Yards," written 5/10/06.)
Little track record
The one extant arena with "of" in its name is The Palace of Auburn Hills, the suburban Detroit arena home to the Detroit Pistons.
In that case, the "of" probably doesn't have the same purpose--rather, "of Auburn Hills" seems to be a way of extending an otherwise short name.