If you are self publishing, you can do what you want, including having control of the cover art for your book. You can design it yourself or you can pay someone else to do it.
But assuming you're talking about traditional publishing, than most often the answer is no. Publishing houses generally have their own "in house" or contract artists. These artists are chosen and paid by the publisher and even then, they may go through many proofs, working with marketing specialists (and many opinions) before choosing something that finally ends up with your book. Granted, there may be a few publishers who take the author's opinions and thoughts into consideration but don't demand or expect it.
Don't be upset! You have that perfect image for your book in your head. You want some say into the inner workings of anything that will affect the piece of literature that you have painstakingly created. I get that. But don't fret! Everything that is done for your book once the contract to publish it is signed, only serves to enhance its sales. And that's really what it's all about. Sales. If you trust your publisher enough to enter into a contract with them, then you need to trust them to do their job with professionalism and without added drama from you.
Peace, happiness, and non-diva attitude,