So I too had this issue. I have not yet tried either of the two things suggested in this thread ... But, I wanted to take some time to report my findings.
I have two MBP retinas, one with device name of "Rich MBP" ... the other named "Rich WORK MBP".
I removed these Plist files (on both Macs), (from reading a few related posts):
~/Library/Preferences/com.apple.ids.service.com.apple.madrid.plist
~/Library/Preferences/com.apple.imessage.bag.plist
Logged out of Messages and back in again (on both mbp's) in order for the plist files to get regenerated.
Things **seemed** to work at first. At this point, MY IPHONE STARTED KEEPING TWO DEVICES LISTED under the messages sms forwarding devices list !! Yeah! (before it would only hold one).
So ... I continued, ... I finished getting handoff / continuity working on the first mac and the device displayed correctly on my iPhone: ("Rich MBP") .
Started working on the second mac for continuity, got things working there … BUT THEN >>> THE FIRST MAC BROKE !!!! Now my iPhone reports two entries for the second mac:
"Rich WORK MBP"
"Rich WORK MBP"
Basically the first entry changed from the correct device name of "Rich MBP" to "Rich WORK MBP" ...
Toggleing the second entry to the ON position (from my iPhone) will cause the numeric code to pop up on the work mbp.
but the first entry will neither, (a) flip back to the correct name, nor cause a code to pop up on either mac.
Here's the kicker.
I open up the file:
com.apple.ids.service.com.apple.madrid.plist to take a look at it.
The first mac is missing an entry for "UniqueID", (yep the generated file is missing that entry) the second mac, that works, had an entry for it with a "UniqueID"
BTW … it's not the same number as the UUID for the administrator account from the second solution in this thread.