In order to split and rename clips in Movie Maker you need to carry out the task using the clip from the collections pane and the controls in the monitor window. You cannot rename a clip split on the timeline.
See here for a video tutorial.
With Movie Maker open and the collections window open you need to select the clip which you wish to split (Left click on it once).
Once selected, it will appear on the preview monitor.
Use the controls immediately below the preview monitor to move the video to the point at which you wish to split it.
Split the clip. See this video tutorial if you don't know how to do this.
You will see that a new clip has been created in the collections pane.
Continue to split each clip to your requirements.
To rename the clips you have three options.
1. Select the clip in the collections pane, press F2, type the new name and press enter.
2. Right click on the clip, click on rename from the properties box which opens, type in the new name and press enter.
3. Select the clip in the collections pane and from the menu across the top of the screen click on clip. Choose properties from the drop down box. In the properties box which opens, type in the new name. Click Apply and OK.
When you press F2, select rename from the dialogue box etc, you will find that the name of the clip is automatically highlighted, so you can just type in the new name straight away. If you click elsewhere before typing, you will need to re-highlight the name of the clip and type in the new name.