I don't think the serial number is part of the CPU itself, but rather part of the logic board, and like MacHead mentions, a logic board swap is effectively the only way to change the serial number.

New logic boards often come with no assigned serial number, and there is a technical procedure required to put a serial number on the board (typically you would put onto it the serial number of the board you are replacing). For good reason, this procedure is generally only known or available to the manufacturer, and not something we as mere mortals have easy access to.

I don't know if you've run across this, but occasionally I've found a laptop that has no serial number, or a serial number typed out in lower-case (typically they are upper-case). This is a giveaway sign of a replacement board, and indicates that the tech was too lazy (or not knowledgeable enough) to put the old board's serial onto the new board, or that they put the number on, but typed it in lower-case. When I was responsible for server environments, Dell techs would always forget to put the serial number back during a motherboard swap, and I would always be annoyed and ask them to come back.

On many PCs and servers, the serial number can be changed in the BIOS, and although I'm not sure, I suspect on Macs it's done in Open Firmware or something similar.