After some testing of my own, it appears that this cannot be achieved in this way as the e-mail item is an object whose properties are predetermined from within Outlook before being pasted into the Word document.
You are looking to treat this object's name - although part of the object / icon itself - as a caption, which cannot be done as it has been copied from an external source and was not created in Word to begin with. Consider - and treat - it as an individual entity whose properties cannot be modified in this way.
However, it is not all bad news and can be achieved via the following steps (which I myself have tested and can confirm the validity of):
- Copy e-mail item from within Outlook
- Paste into a separate location on your computer (desktop will suffice)
- Rename the object on the desktop
- Copy newly-renamed object and paste into Word document
Please note that you may lose the icon in this process, which should be easy to restore.
I hope this helps.