The costs and process to legally change your name varies state by state and county by county. You can do an online search for businesses that can guide you step by step through the procedure, or you can visit your county clerk department for precise instructions and information.
In order to chnge your name it doesn't cost anything, just tell people call you by your new name. Unless you want to change your name legally then on average it would usually cost about $100. For more information you can contact your local government.
It depends on the filing fee with the County you live in. I know that to obtain the name change forms (technically "name change petitions") it usually costs around $100 from legalzoom and http://howtochangeyourname.com