Under the Scale menu there's an option to "Label Axes with measure names" however this only applies to Y-axis labels which is understandable given that this is in the Scale menu. Is there also an option to show/hide the x-axis label which only seems to show up when mutliple measures are selected? It would only seem fitting that this option would be available under the Measure menu.
In the attached image you have both X axis (split) label, and Pane labels. Both can be removed. Under the Split menu, the last item in the row next to your split field (Month in this case) is a little triangle. When you click on it, you will get an option to hide labels. Similarly, when you click on the X axis Pane option, the triangle next to the word "Measures" will enable you to remove the pane labelling.