How can I modify the My Computer text to show logged on username and machine name?

Start the registry editor (regedt32.exe)

Move to HKEY_CLASSES_ROOTCLSID\{20D04FE0-3AEA-1069-A2D8-08002B30309D}

Select the value and Delete

From the Edit menu select 'Add Value'

Leave the value name blank and set the type to REG_EXPAND_SZ

Click OK and enter the text
User: %USERNAME% on: %COMPUTERNAME%

Click OK

Click on the desktop and press F5 (for refresh) and the change takes effect

Start the registry editor (regedt32.exe)

Move to HKEY_CLASSES_ROOTCLSID\{20D04FE0-3AEA-1069-A2D8-08002B30309D}

Double-click the value LocalizedString to edit and cut'n'paste the contents to somewhere safe. It will be something like:
@D:WINNTsystem32shell32.dll,-9216@1033,My Computer

Use Registry/Save Subkey to save the current entry.

Delete the value LocalizedString.

Create a new value named LocalizedString of type REG_EXPAND_SZ and paste in the content saved at step 3). Edit the text 'My Computer' at the end of the string and change it to '%USERNAME% on %COMPUTERNAME%', for example to:
@D:WINNTsystem32shell32.dll,-9216@1033,%username% on %computername%

Right-click on the desktop and choose Refresh, if you have desktop icons shifted to the taskbar, right-click on the desktop section and choose Refresh.