Who owns the copyright for my book cover design?
There are multiple answers for this question, and they all come down to agreements between you, the designer and your publisher.
If you have commissioned the design and been instrumental in the design process all the way through, then the copyright could very well belong to you. To make sure, you need to stipulate in the commissioning contract that the artwork once it is completed belongs to you.
Designers, as a rule, are the ones who own the copyright, and the fee you pay them is for the right to use that design on your book. Even if the designer is hired by you, your published (or employed by the publisher), the copyright still belongs to the creator of the design.
When the cover design includes branding elements belong to you or your company, they become part of the overall design. It is the overall design that belongs to the designer NOT your branding elements.
Some publishers stipulate in their contracts that the cover design is owned by them. If you wish use the designs in anything other than the marketing materials provided to you, then it is common place that you will need written permission to use the design. For example, if you wish to create bookmarks, journals or other items such as branded merchandise, signage for events etc.
If you wish to own the copyright for your book cover and marketing materials, it is always best to stipulate this when beginning the working partnership. You may be asked to pay more for the ownership, and it is always a great idea to make sure you check the current laws in your country at the time of commissioning work.
There are many organisations, such as the Society of Authors, who have legal teams on hand to advise you on subjects such as this.