Just to make sure that you don't abuse the components properties: I suppose you want to select some directory. You get this directory from the FileName property, rather than from InitialDir (I admit that naming the selected directory "Filename" is a bit unusual and misleading...). InitialDir is the directory for which the subfolders are displayed - just look at the dialog in the same way as you look at the standard TOpenDialog (from with TSelectDirectorydialog in fact inherits), with the only difference that the "files" now are "directories".
Example: you want to select a directory from /etc. Therefore, you set InitialDir to /etc, and you pick, for example, "lazarus" --> Filename will be /etc/lazarus, InitialDir will stay at /etc.