Creating polygons from open ended line (riverine) feature

I have a dataset of rivers which I’d like to build into polygons of areas enclosed by rivers.
The rivers are continuous lines but there are open ends.

Is this possible? It’s OK if the calculated boundary between the open aspects of the rivers is less precise, and it doesn’t matter if the process causes gaps or forms a homogeneous polygon, either is OK.

Currently I’m drawing them by hand using the trace tool. I tried grouping by river/feature name but this wasn’t successful. I also tried minimum bounding geometry, both as lines and converted to points, and if I select the points manually then it’s fine, but I have no way to group them as again the name isn’t helpful.

Is this possible, or should I carry on tracing?