Let's go back to the first image, in your first message above. In this dialog, I would fill in only three fields:
Name: This is the name that is shown in the accounts tree in The Bat (so, not important here).
Fr om Name and
From Address: These two put together (with the address between <>), make the 'From' field in outgoing e-mail.
So, if you keep 'Domine Ingles' as the From Name, and use (for instance) '
[email protected]' in the From Address field, then the From field in outgoing e-mails should become: 'Domine Ingles <
[email protected]>'.
I can think of only two ways how this can go wrong:
1) Maybe the receiving e-mail client (or webmail host, like your Yahoo) is changing how the From field is shown. But in this case, that can't be it, because it happens with all accounts wh ere you sent your test message..
2) In The Bat, look in Account | Properties | Transport. As you probably know, the 'SMTP Server' shown here is the server through which your messages enter the internet. Some SMTP servers actually change the From field in your e-mails, and replace it with the account details that they have on file for you. Gmail for instance does this (or used to do so - I don't know if they still do it). So, if the details that you have entered in The Bat are not shown to the recipient, then I think that this might be the explanation. If so, see if you can change the name in the setup of your SMTP provider, or use a different SMTP server for outgoing mail.