Domain Name Change Of Url From Smug To Faa

Hi folks I need to eliminate my smug mug site and only work with FAA and Redbubble as all I get from Smug Mug is views and no sales over several years of time. My question is this I'm a little ignorant of how this domain name thing works my name there was listed as branhamphoto but here it's randallbranhamphotos I would like to keep branhamphoto as it seams to be shorter and possibly easier to remember ,but most importantly it is well known on the search engines. How and what do I have to do to accomplish this , remember I need very detail info I went to go-daddy that's where my domain name is registered,but I don't know if smug mug has control of that or if I do. thanks for all your help in advance Randall