Is there reason or the status of the state to able to put the word "the greater or the great" to its name?

Question

such as the Greater Los Angelos or London

or Great Britain

or formerlly the Greater Germany, Syria and Finland

Answer 1

The term "greater" usually describes both a city and the associated areas around it.  The Greater Los Angeles Area, for instance, refers to both Los Angeles proper and all of the smaller towns and suburban sprawl surrounding it.  The term "Great Britain" is used to describe the largest ("greatest" in size) of the British Isles.