It appears that this might just be a red herring, after all: While the default address displayed in the 'From' field is the 'User Name' (from the 'Logon Information' section of the Change Account dialog), it seems that the actual mail sent out uses the 'Email Address' (from the 'User Information'), which is what I want.

In OL 2003, the display of the 'From' field was blank, which never worried me, since it means intuitively that the default will be used. Apparently when they decided to put a name in the box, they must have made a strange choice to use the logon name. I don't see the logic behind that choice, but I can live with it – if that really is the explanation, and if it works reliably.