It is unclear to me how you got from your input data to your expected output. If you are "trying to count() overlapping entries" then it would seem to me that you would only have only one value for the count. Either a range overlaps or it does not.
All 'a', 'b' and 'c' have points in common, with count a=3, b=1, c=3.
Thanks.
I think data are not correct...
Expected result is the same as count() group by name...
But I guess you have included name column just to different ranges for overlap...
But actually there is just 2 ranges:name b is 1 range, name a & c are second range. all overlaps by first range '2015-12-20, null) - it contains all records named as C ranges