Building a capitol on a planet changes your home planet to the planet where you built the capitol. You may only have one Capitol per empire. Your home planet is immune to the spy missions Insurrection and Appropriate Technology. In addition, through the use of the Stockpile, you can build resource buildings past level 15 on your Capitol planet. As an added bonus the capitol produces a small amount of additional Happiness.
You can rename your empire through the Capitol's Rename Empire tab. The cost is 30E; however, this cost is adjusted down 1E per level of your Capitol.