It looks like your label is based on the “NAME_0” column and not a column that contains the district name. You can correct this by clicking on the label tab of the map ribbon when you have the proper feature selected in the contents pane.
But when you assign the correct column as your label, you will want to apply scale restrictions, or possibly classes, due to the length of the district names.
Here are some ESRI documents that should help with your labels: