carlosray1 on "Transferring to Word Press.org"

If I have a Word Press.com blog and want to transfer it to a full Word Press.org website (I have already bought a Word Press compatible theme that was purchased at http://www.themeforest.com), can I use the theme I bought with the transfer and can I still keep the same website name?
Blog url: http://carlosray1.wordpress.com/