that must be really frustrating - especially as the others work! I tried to keep a track of all I did on an email draft, but maybe some was just intuitive and/or luck. This is what I saved, if it is any different:
You must register your phone number by signing into iMessage from your iPhone. If you are already signed into iMessage on the iPhone, sign out and sign back in on the iPhone.
If it still doesn't appear on the computer, sign out of iMessage there and sign back in. It should appear then.
Also, in order to send SMS messages from the computer, you must enable it on the iPhone. In iPhone settings, open iMessage. Select Text Message Forwarding. You must be on the same wi-fi network. Your computer or other device should show in the list. Just click on the device you want to enable.
Also enable SMS on the iPhone.
See the answer in context
2. Messages/Accounts/Message Account/Settings - click add e-mail and enter the phone number.
3. Open Messages, click Messages>Preferences, open your Apple ID account within, on Settings tab add phone number in "You can be reached for messages at:"
in response to blackdogaudio
yes, but first I had to do a number of actions. Not sure if the order is correct, because I was just feeling around, trying to follow leads, and see what worked.
-open MMS in Messages under settings, so here Apple sent me a passcode which appeared on my computer screen, saying something new was going on, and did I approve
-then make sure the persons phone number was IN contacts, went to
-Messages/Accounts/Message Account/Settings - click add e-mail and enter the phone number.
-then in Message, open Preferences, Account and switch on (somehow I had switched it to this 'Bonjour' thing. who knows if that is what made a difference.
But voila! green name on messages, green, and message FINALLY delivered.
strange that it had worked for months and months, using my iphone5, but maybe stopped when I got the iphone6, and they did not tell me everything had to be closed and opened again.
Whatever! who knows, when one contact's phone did not relay messages properly it was dumbfounding, and I solved it. My son was not impressed with my ingenuity, no doubt figured it was just the old one dumbly wandering around, but it seemed to me it took about 4 or 5 separate interactions, and Apple support was no help. Keep googling your problem.
At one point - probably the crux: a message popped up on the computer that someone was trying to use imessage from a new device, and gave me a code.
so you need your computer open at the same time that you are working these settings. good luck.