Normally, if the boinc client reconnect the cpid, if changed, is updated automatically by the boinc server software. If not, you can also merge the computers manually in the host list.
To update the new cpid at the other projects the computer is crunching for, you must connect one time at these (you need not to download any wu's there), so the boinc server software from the other projects notice the new id.
I also recognized this problem with the new 6.12.X boinc client, in my case, i only add an additional graphics card in the computer. I seem to remember, this was not a problem with the old one.