Again I assume you are using KDE and I refer you to this thread
. The OP has a remarkably similar problem and a remarkably similar posting style.
Anyway in this case you would want to edit the file "Home.desktop" instead of "trash.desktop".
...(lots of other names for different locales)
This is what Home.desktop looks like for me, so I would change the third line "Name=Home" to "Name=My Computer".
As pixellany said Home is not really equivalent to My Computer in fact you might want to rename the "System" link rather than "Home". If thats the case then you want the "System.desktop" file.