At the top right of the Thunderbird window, click the menu button > Options > Display > Advanced tab. Check 'Show only Display Name for people in my address book'.

I've been there and tried it before without results. In my address book are three kinds of name: First Name, Last Name and Short Name. I'm not quite sure which of those you call the Display Name, but it seems to be ShortName. The box "Show only Display Name for people in my address book is checked". But the email address remains. If I do not enter anything in Short Name at all, only the email address appears What am I doing wrong? /hans peter

In my address book are three kinds of name: First Name, Last Name and Short Name.

In the address book there is First, Last, and Display. Display needs to be populated. Nick name is irrelevant here.

I have entered a name in Display Name but the mailaddress remains. /hans peter

Did you restart Thunderbird?

Yes, several times :-)

I thought the Display Name option was designed for incoming messages. I don't think I've ever seen it working when addressing a message. If it did, I'd be able because some of my Contacts have multiple email addresses and I need to know which one will be used.