There are several American zoos that are three words long because they are named after the park they are in. Just name it after the city instead is my advice. Not only will this shorten it to two words (unless the city name is two words) but it will also let people outside the region know at a glance where exactly it is. Here are a few, but there are lots more.
Reid Park Zoo (change it to Tucson Zoo).
Cameron Park Zoo (change it to Waco Zoo).
Dickerson Park Zoo (change it to Springfield Zoo).
Lowry Park Zoo (change it to Tampa Zoo).
Lincoln Park Zoo (change it to Chicago Zoo).
Woodland Park Zoo (change it to Seattle Zoo).
Seneca Park Zoo (change it to Rochester Zoo).
... and so on.
Chicago Zoo would not work because Brookfield is just outside of Chicago and was called Chicago Zoological Park in the early 1900's.