For those who want to play as a default race(without copying) and want a different logo this 7 step Program:
1.Locate FactionDefs.XML
2.Open with Notepad,Notepad++ or other alternative
3.Locate(ctrl+f)chosen race EG:Drengin
4.Look for <LogoImage>RaceLogo01.png</LogoImage> and delete anything within <LogoImage>This space</LogoImage>
5.Find a logo you like from your Documents>GC3>Faction>Logo Folder and copy its name(include .PNG)
6.Go back to your opened XML and <LogoImage>Copy here between the</LogoImage>(No spaces)
7.Save XML and load up GC3 and enjoy your new Drengin's(etc) with a nice new fluffy bunnies logo(or what ever you choose)..

Above image my terrans with systems alliance logo from ME series
Remember ALWAYS backup BEFORE making Changes to the games XML files..(i have originals 7zipped "just" in case)
it is probably possible to do this as a mod so that you do not have to touch the default game XML file(other than copying it of course) but i am fairly new to XML editing(and modding) and am not 100% sure how to do it that way..
Edit (You can use Custom logos from GalCiv 2 or make your own if you are creative)