From what I can glean, "hatchee" means "river" or "river of the" in the local native dialect.
For example, the first paragraph of this article:
Likewise, from the last paragraph in this article:The Choctawhatchee is a river arising in southern Alabama and flowing about 225 km (140 mi) south into northwest Florida, where it empties into Choctawhatchee Bay, an inlet of the Gulf of Mexico. In its present form the name simply means "River of the Choctaws".
In 1931 the community was renamed Steinhatchee after the river. The name Steinhatchee was derived from the Native American "esteen hatchee" meaning river (hatchee) of man (esteen).