To label each line we need a cell range with the same size as the chart source data. Simply copy the chart source data range and paste it to your worksheet, then delete all data.
All cells are now empty. Copy categories (Regions in this example) and paste to the last column (2018).
Those correspond to the last data points in each series.
Right-click on a data series and select "Add Data Labels".
Double click with left mouse button on one of the data labels you just inserted to open the task pane window.
Select checkbox "Value from cells".
Select data label cell range we created earlier in step 3 and 4, that corresponds to the same line series. Use the legend to identify line series.
In this example the data labels correspond to "South America", see image below.
The data labels now show both numerical values and the last text value.
To hide the numerical values simply double click on the data labels to open the task pane.
Deselect check box "Value".
All numerical values are now deleted from the data labels, only the last data point has a data label, see image below.
Position the data label to the right of the data point using the task pane.
Resize the plot area so the data label doesn't collide with the line.
Repeat step 4-12 with remaining line series.
How to wrap data label text
Double click on the cell that contains the data label.
Put the prompt between the words.
Press Alt + Enter.
Align data labels
If you want the labels to be aligned to the left simply select the data label.