usually just "District Line", "Bakerloo Line" etc, as the lines in both directions are generally close to each other. But as you get nearer they often have to differentiate, as in the Jubilee Line signs I mentioned (in some stations the lines are actually on different levels), so they may say Jubilee Line Eastbound" and "Jubilee Line Westbound". They don't give the terminus stations the way they do in Paris, as trains often don't go right to the end of the line.
In the case of the District Line they sometimes use several platforms (as they may share them with other lines), so you might need to look for larger signs which tell you which one to go to for the next train heading for your destination. Sorry I don't know those stations well enough to be precise, though.