'Undisclosed Recipient' is applied by TB when you Bcc a mailing list and there's no entry in the To: box. If you enter your own address in To: and then enter the mailing list or other contacts in the Bcc box, you can avoid this.

http://kb.mozillazine.org/BCC

I am not using BCC, the mailing list is used in To:

I'm not aware of 'Undisclosed Recipient' appearing in TB unless mail is sent Bcc, so I can't explain why you see it with To addressing. Perhaps it's inserted by the mail provider when a message is sent to a mailing list.

Checking further, i discovered that if i view sent mail, every email shows it's From:"Undisclosed Recipients" regardless of whether it was sent to a list or an individual. There has to be an error in TB causing it to happen. I rarely use BCC.

If you open Tools/Account Settings, select an account in the left pane, is there an entry in the Your Name box, for each account and identity?

Yes there is a name for every account.

Do you have any identity-choosing add-ons? In fact, to see if any add-on is causing this, run TB in safe mode (hold Shift when you launch TB).

Do not see any add-ons in Safe Mode.

Sorry, a better check showed Duplicate Contact Manager and Lightning as ad-ons.

Disable Duplicate Contact Manager and see if that makes any difference to your outgoing identity.

Disabling the Duplicate Contact Manager made no difference. However, I did some experimentation and found that in my sent file, From: always showed from Undisclosed Recipients. If I removed Undisclosed Recipients from my address book, From: shows as: Me<my email address>. I have restored Undisclosed Recipients in the address book until I hear back from you as it has it's uses. I believe the recipients actually see the correct sender's information. I appreciate your diligence in helping to resolve this issue.

I've never heard of Undisclosed Recipients appearing in an address book, and I don't know why it was appearing in your sent messages, unless the address assigned to it was your own. I suppose it could be entered in Collected Addresses if you Bcc a mailing list, but as mentioned above, it's possible to eliminate it by adding your own address in the To: box.

There are instructions on the Internet from Mozilla and by Livewire clearly instructing: to use "Unidentified Recipients" create entry in address book for same with user's email address.

I notice this lifewire link about Undisclosed Recipients, which I would call misleading, but cannot find any official or authoritative source, such as the one in my first reply, that suggests you create an address book entry. In view of the confusion it causes, perhaps this misconception should be laid to rest.

I will take your advice, delete the entry in my address book, follow you original reply's method, and trouble you no more.

Many thanks for all your efforts to help me resolve this question.