How about we just get rid of the names in the `str()` version?
```
air_potential_temperature / (K)     (6, 70, 100, 100)
     Dimension coordinates:
          grid_latitude              -   -    x    -
          grid_longitude             -   -    -    x
     Auxiliary coordinates:
          level_height               -   x    -    -
          sigma                      -   x    -    -
          surface_altitude           -   -    x    x
     Derived coordinates:
          altitude                   -   x    x    x
     Scalar coordinates:
          forecast_period: 0.0 hours
     Attributes:
          source: Iris test case
```
But for the `repr()` we keep the dimension coordinate names:
`air_potential_temperature / (K)     (6; 7; grid_latitude: 100; grid_longitude: 100)`

A possible extension would be to add the axis name to any anonymous dimension where the auxiliary coordinates don't disagree on what axis is relevant:
`air_potential_temperature / (K)     (6; Z: 7; grid_latitude: 100; grid_longitude: 100)`
`air_potential_temperature / (K)     (6; "Z": 7; grid_latitude: 100; grid_longitude: 100)`