Actually most cities with a significant Jewish population have their own Kupat Ha’ir.
In Chicago it is called ARK. In Dallas it is called Jewish Family Services.
As Jews we can not agree about Shabbos or Kashrus or other issues. But the one Mitzvah we all agree upon is Tzedakah. One Mitzvah that all Jews agree upon in a city can be a tremendous merit for the whole city.
So if your city has no Kupat Ha’ir and you have the means to start one, do so. Call it whatever will generate the most local support.