So yes, naming is one of those qualitative things, but the term 'Gatherer' doesn't sound great to my ears, and introducing a new 'Integrator' term to represent the Gatherer equivalent of a Collector's accumulator doesn't seem necessary either.

In terms of streams, it seems like this is a fancier 'pipe' ( in unix terms ), so I would have called it .pipe() instead of .gather() ... having a series of .pipe()s seems more intuitive than having a series of .gather()s on a stream.