Note that if you're running Windows 7, the location of the working copy of Alpha Centauri.ini is in
C:\Users\(user name)\AppData\Local\VirtualStore\Program Files (x86)\GOGcom\Sid Meiers Alpha Centauri
and NOT in C:\Program Files (x86)\GOGcom\Sid Meiers Alpha Centauri.
You will find an AlphaCentauri.ini in both locations but only the one in your AppData will be used! You can check this easily by saving a game and then when you open both ini's one will have the save game name in it, the other won't.
My Windows 7 stores the *.ini file in the installed game folder (in this case, an external drive), thus:
G:\Games\GOG\Sid Meier\Civs\Alpha Cenauri\Alpha Cenauri.Ini
As far as I can tell, there are no other copies of this file on my system; it is the file that was updated with save game names.
Perhaps you meant a different version of Windoze?