First thing you'll need to do is create a label style. The general line label styles are found on the Settings tab of your workspace -> General -> Label Styles -> Line. Right click on Line and select New...
Give your new label a name. In this example, I'm creating a label for the end of the line so it's called "End Elevation" (original, I know). On the layout tab, go ahead and remove all the components (select the component name and hit the red X) so we are starting with an empty style.
Now, let's go ahead and build the style. If you've looked at the anchor components, one thing you'll notice is there is no apparent way to attach a piece of text to anything other than the anchor point; which is the middle of the line. Well, we can get around that fairly simply. What we need is a component that goes from the start point of the line to the end point of the line and the component that does that is the direction arrow. So let's go ahead and add the direction arrow to our label.
A couple things to keep in mind. First, we don't want to see the direction arrow, we just want to use it so make sure to set the visibility to false. Second, we want the direction arrow to go from the start of the line to the end of the line so make sure the fixed length is also set to false. Now that have the start and end points of our line, via the direction arrow, we can attach text to them.
A couple notes on this component. We want the anchor component to be the direction arrow and the anchor point to be the end. This will place the label at the end point of the feature line. Now, we need to compose the text value of our lable. Click on the ellipses (that's the three little dots) in the value cell for the text contents to bring up the Text Component Editor.
For the text properties, we want to use the General Segment End Z, format it how ever you like, and then hit the blue arrow to insert it into the label. That's all there is to it. You've just created a style to label the end points of your feature lines. You'll probably need to repeat the process to create a label for the start point, as well as labels for the start and end of curves. Now, when you want to add the label, simply go to the General menu, Add Labels... and select Line and Curve for your feature and the styles you just created for the label styles and away you go!