Does anyone know a way to rename an existing shortcut?

I am installing an update. The initial full install has already placed a
program shortcut called "My Shortcut" on the program start menu. I would
like to rename this existing shortcut to "My New Shortcut".

Deleting the existing one and adding the new one would work just as well,
however, I have been all through the help file and functions and can't see
any way to do this.

Is it possible?

Thanks.

Lee