`Cube.metadata` is currently (i.e. on `master`) used:
 - to simplify the transfer of all the Cube metadata during copy-like operations(*),
 - to simplify the comparison of metadata in the `==` operator,
 - to determine compatibility within the merge process.

(*) e.g. `Cube.__getitem__()`, `Cube.copy()`, and `iris.analysis.interpolate.regrid()`

So there's a simple story that says `Cube.metadata` is all the non-coordinate metadata for a Cube. Hence `var_name` should be included. In which case, the only place that might need subsequent work to deal with this is the merge process - but that's because it's performing CF-aware metadata transformations, not just a simple copy, so I'm happy with that.