What you're talking about is known as the "display name". The real email address needs to be there to allow the email system to deliver your messages, and the system has no use for the display name; it is included just for users' convenience. Therefore the email address will be included anyway. So why hide it?

Some mail clients do this cosmetic tidying up and seem to mislead their users into thinking that this will stop a recipient seeing the other recipients' addresses. But no, those addresses are in the message headers and can be found.

Thunderbird is carefully trying to be honest with you, and explicitly shows what data will be included.

There are settings to control how Thunderbird displays to you, and it can be set to show you display names, or the corresponding entry in your own address book, but we have no control over how this data is displayed to the recipient.

Thank you but that's not what I was asking. I'm not talking about how the addresses are displayed to the recipients. I realise that the recipients of the email are going to be able to see the email addresses. I would just like, for cosmetic reasons, for me, the sender, to see only the name in the To: bar, rather than both name and email address. My understandng is that Display Name only comes into play when *receiving* emails - certainly it seems to have no effect when I'm selecting recipients for an email I'm writing. That would be an ideal solution - for the To: box to use the Display Name if it's present.

Sounds like you like to live dangerously. Do none of your correspondents have multiple email addresses and so you have no need to check which account you're sending to?

I can see which name/email address combination I'm choosing when I select them from the dropdown address list. After I've made that selection, I no longer need or want to see the address in the To: bar.