Version:            (using KDE KDE 3.5.3)
Installed from:    Compiled From Sources
Compiler:          g++ (GCC) 4.1.1 20060525 (Red Hat 4.1.1-1) 
OS:                Linux

The member names are being displayed on the association lines!

For instance if you have:

class A
  private:
    B memberClass;

When you place both class A and B in your diagram, class A shows the attribute "memberClass", but ALSO on the drawn composition line is the text "-memberClass".  If you delete it, the text returns the next time you open the program.