At the top right of the Thunderbird window, click the menu button > Options > Account Settings

Select your account in the left pane.

Make sure the field 'Your Name' is filled properly.

yes, my name is there, but thanks for mentioning - I should have specified that my name is correctly provided in the Account settings.

BTW, I have reason to believe that my name is being sent to my email recipients. I just don't understand why Thunderbird is not showing it to me in the sent emails in my Sent box (so that I can see what they see)

What do you actually see?

my email address only

Do you have your own email address as a contact in your address book? Make sure to set a display name.

Hmmm. Yes, my own email address is in my address book with that email address in the Display field of the entry!! i think this is/was the problem! Thank you! I should have thought to look at the address book.

I have just one more question. When I send an email now, what I am seeing in the From field (of the copy in my Sent folder) is "Me <my email address>" Does this mean that Thunderbird recognizes the From email address as the one I've identified as mine in the Account settings and is just substituting in the From field of my sent emails the character string "Me" to signify this? Whereas what my recipients see in the From field of the emails I send them is the Name I have specified for myself in the Account settings?? I'm guessing (for now) that this is the case. I would REALLY prefer, however, that Thunderbird simply put my Name in the From field of these sent emails for my benefit as well so that I am seeing in the From field exactly what my email recipients are seeing!!

Thanks again for you help with this question. It really had me stumped!

At the top right of the Thunderbird window, click the menu button > Options > Display > Advanced > Display

Uncheck 'Show only display name for people in my address book'.

wow, this is what I've been looking for! Thanks again so much. In retrospect, I probably should have been able to find this myself! I've been using Thunderbird for a lot of years and obviously there is still a lot I don't know about it! In the future, I'll try to dig around more before I come back to this forum. You've cleared up a vexing mystery for me! :)