Am using newly installed LibreOffice 4.1.6.2 English UK) as replacement for OpenOffice in Win XP Professional (SP3). It may be something I altered in options but I haven’t found the answer.
Most of my files are ODT but some are DOC, WPD and RTF.
If you double-click on an existing file from File Manager, doesn’t the “real” name appear in the title bar? For me (Ubuntu), “Untitled 1” only comes up if I start Writer without “specifying” a file, or if I click on “File > New text document”.
How do you “open” the file, e.g. Right-click > Open, Double-Click, File > Open, drag to title bar? What is your setting for “Use LibreOffice Dialogs” in Tools > Options > LibreOffice > General > Open/Save dialogs?
@JBachS - thanks for the update - and good to know you sorted it! One suggestion: beneath your comment there should be a link that says “convert to answer” - please do this so your solution will be more visible to others who might have this problem. Also, it means we can “up-vote” your reply. 
Thank you David and Regina. Problem solved. If I double-clicked on the file in My Computer it would open Untitled 1. If I right click I have now found that I have options including to open the file I want to open or to simply open Writer. I checked the settings you pointed me to Regina and found that I had checked Open Save Dialogs which meant nothing to me at the time. However I unchecked this and consequently the programme opens by double clicking on the file as I have always done. I had previously googled and found a number of people had come up against the same problem without finding a solution. Although it is obvious to me now what the Open Save dialogs means, I think the option needs to have a “further information here” added. I’ve used word processors right back to Wordstar, but unfamiliarity with a new programme can mean that a bit of computer jargon doesn’t impinge as immediately as one might expect.
Thank you again.