It is easier to tackle this question in two folds:
- i) which tool (if any) does such type of GIS operation in one step;
- ii) what is the standard terminology for it.
The Union tool from ArcGIS Desktop does exactly what is described in the Venn diagram when the input features belong to different/separate files/layers. For example, polygon A is in one file, polygon B is in another file. It will create from those two overlapping polygons, tree polygons in the output:
- A without AB intersection,
- B without AB intersection and,
- AB intersection.
The attributes from them will be joined, meaning AB will have attributes from both polygons A and B. See from How Union works article:
The output feature class will contain polygons representing the geometric union of all the inputs as well as all the fields from all the input feature classes. ...
On the other hand, the
Union tool will work in a different way if overlapping features belong to the same input file/layer. In this case, it will create four polygons in the output:
- polygon A without the AB intersection,
- polygon B without the AB intersection,
- AB intersection with attributes from polygon A,
- AB intersection with attributes from polygon B.
So, in other to achieve the result expected from the Venn diagram, one would need to stack attributes from intersection, and delete one of the duplicates. Still from How Union works:
Tip: Union can run with a single input feature class or layer ... The area of overlap will always generate two identical overlapping features, one for each of the features that participates in that overlap.
ii) Terminology (of a GIS operation/task):
On the other hand, it seems there is not a standard name adopted to produce that output of a Venn diagram.
Union is not consistent at least across some GIS software. For example,
ST_Union from PostGIS will work like tools
Merge from ArcGIS where there are overlapping polygons.
The most close standard terminology for a GIS task I can think of to describe a Venn diagram output are the complementary tasks of Intersect and Symmetrical Difference on overlapping polygons.