Kinda of a way to do it. 

Click on the race in the race select and copy. Then work with the copy and use that in the game instead of the vanilla

I Know that but when I have Sol for my Star and Earth for my Home Planet, it calls my Star Earth and Planets Earth 1 Earth 2 and so on

Its not that different to moding Civ4.

Take a look at this Test Mod

You need to edit one line in the GC3GlobalDefs.xml to point at the system/systems Group you make for them to show up in the faction creation screens. Search for Horemvore in said file to see what I changed. (Instead of the default ones, if you want the default ones to show make a copy of them from the vanilia systems file paste that in your group and change the Internal name, just add 01 to each one will do)