I believe you are on thin ice here -- sit down with an attorney that deals with patents and trademarks law to make sure you're not going to be in jeopardy.
In no way am I offering you legal advice, and in no way has my comment created an attorney-client relationship. You are not to rely upon my note above in any way, but insted need to sit down with counsel and share all relevant facts before receiving fully-informed legal advice. If you want to be completely sure of your rights, you must sit down with an experienced criminal defense attorney to be fully aware of your rights.
Q: "Am I able to name my company's products after book characters, places, or their authors without infringing on trademarks?"
R: No. More precisely, you may not do so without creating an unlawful "false association" between your products and the book and its author. You can read a court decision that explains this law via the link below.
Q: "I want to draw inspiration from my favorite books and create products using that inspiration. My products may include a story of where the inspiration came from which would include the name of the book and the author. Provided the names I want to use are not trademarked, is this ok to do?"
R: Maybe. We all draw inspiration from what others before us have created. But when you're inspired to create a product and then expressly tie that product to another's work of authorship that you claim was your inspiration then there's a very real possibility that consumers will falsely believe that there is some relationship or association between you or your product and the work of authorship or its author. The law prohibits the creation of that false association in order to sell products.
So ... in general, no, this is not a good idea. But perhaps by working with your own intellectual property attorney the two of you can figure out a way to do so lawfully. And your attorney can always ask the person who owns the copyright and/or trademark in the work of authorship for permission.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
Anytime you endeavor to invest in a trademark you need to conduct the proper due diligence (clearance) on those marks to ensure that you are not in conflict with another (see link below for more info).
While it is possible, of course, that you may be able to use a character's name from a work you really like as the brand name for your new product, it may also be possible that it is already a trademark in that class or in another related class of good or service.
Further, and as my colleague noted, what you described is a good way to get sued. You cannot create a false impression that you are somehow associated with or endorsed by these other works whether they are movies, books, characters, etc.
I suggest you consult with a lawyer in private so you can get some more specific guidance here. Most of us here, including myself, offer a free phone consult.
The law firm of Natoli-Lapin, LLC (Home of Lantern Legal Services) offers our flat-rate legal services in the areas of business law and intellectual property to entrepreneurs, small-to-medium size businesses, independent inventors and artists across the nation and abroad. Feel free to call for a free phone consultation; your inquiries are always welcome: CONTACT: 866-871-8655 Support@LanternLegal.com DISCLAIMER: this is not intended to be specific legal advice and should not be relied upon as such. No attorney-client relationship is formed on the basis of this posting.