Two questions are posed above: Do you need permission, and what are the legalities?
No you do not need permission, however, you shouldn't be doing it for free.
If you only use the name in a favorable way, no problem. Unfavorable and you can get into heap big trouble.
I'm chiming in here because it is not uncommon to be paid by major corporations, or even smaller operations, for promoting their products.
From an advertisers point of view, the cost per thousand is so minimal, they jump at the chance for another place to see their name mentioned.
You do not have to be a best selling author to be considered, but it is doubtful you will make much if your book does not sell well. Advertisers don't waste resources on nickel and dimes. But many will cut a check for three or ten dollars, if your book sales warrant same.
Currently the most lucrative advertisers for authors are the liquor, beer, and tobacco industries. Followed closely by footwear, and internet based businesses.
Many already have simple contracts available that show the amount they pay, either as coinage or a percentage of the books price, and the number of books, or pay level reached before they pay anything at all. Some are as few as 250 books, some pay at 500 books, and a few do not pay until you cross 1000 books sold. The latter is actually the better deal, because the percentage goes up along with book sales. A half-penny per book may not sound like much, until you cross 1000 books and it jumps to 3 cents per book for the next 10,000 books, or jumps to a nickel at 25,000 books. The higher you move on the charts, in some cases, the higher percentage an advertiser pays. Some are simply a fixed amount.
So, if you are intending to use a name brand in your book, and in a favorable light, check to see if the company offers a contract for authors, and if so, send them at least the pages before and after their name is mentioned, and the page it is mentioned on. If you have previous successful book sales, provide your rankings and book sales information, as this can up the amount they offer.