Open iTerm2 preferences by using the keyboard shortcut, Command + , or by invoking the command iTerm2 → Preferences... in the Menu Bar.
In the preferences window, switch to Profiles tab and under Working Directory select Advanced Configuration. (The default selection is Home directory.)
Now, click on the Edit... button, and in the pane that opens, under Working Directory for New Split Panes select Reuse previous session's directory. (The default selection is Home directory.)
Now, when invoking the Splitting Vertically with Current Profile command by pressing Command + D keys, the adjoining window will be opened with the same directory as the current working directory.