The first thing you should do is to meet with a patent attorney who has experience drafting patents in the area of your invention. Many patent attorneys offer an initial free consultation to determine your goals, what your invention is and how best to protect your invention to meet those goals. The patent attorney should also be able to assist you in protecting the name of the product with a trademark.
Bear in mind that not all patents are created equally. An experienced and knowledgeable patent attorney will likely draft a much better patent than a patent attorney with less skill or experience. A better patent affords you broader coverage when carving out you monopoly, making it difficult for would-be competitors to "design around" the patent and compete with you.
A better patent is also more defensible in court. Even tiny mistakes in the patent application process can lead to the patent later being held invalid and unenforceable. You may want to consider hiring a patent attorney with a solid track record of defending patents in court. Patent attorneys who have successfully defended patents in court know what they like to see in a patent to avoid invalidity and prove infringement.
The goal is to obtain the best patent possible. In the event an infringer appears, a broad defensible patent will increase the odds the infringer will enter into a license agreement, rather than force you to sue them in court. It is important to set an initial consultation with a patent attorney as soon as possible, as both patent and trademark rights can be lost if you delay.
The below does not constitute legal advice, does not form an attorney-client relationship, and should not be relied upon to take or refrain from taking any action.
As Brett notes, you need to meet with a patent attorney.
In my opinion, however, it is not only very helpful for you to do some homework before that meeting, it is your responsibility. Everyone invents something. The vast majority of "inventions" are not patentable and, even if one is, it may not need patent protection to be successfully exploited in the marketplace. Your goal is not to acquire a patent but rather to make money by either selling your gizmo directly or licensing to someone else the right to sell that gizmo.
Before speaking with independent inventors I prefer they read the books "How to License Your Million Dollar Idea," "From Patent to Profit," and "Patent It Yourself." And then to come in to discuss their invention and business plans. Anyone who chooses not to demonstrates to me that they don't have the stamina, interest, or passion necessary to see through what it takes to turn an invention into a product on store shelves. Good luck -- I hope your invention is one that becomes profitable.
I've met with many people that have sabotaged their chances of patenting their invention by disclosing the invention without a confidentiality agreement in place, and then sitting on it too long before moving on the application.
The longer you wait after your idea is ready, the greater the chance that someone else will have the same idea and get to the patent office before you. There are some documentation steps you can take to help you in case that would happen, but it is a potentially expensive and uncertain battle that can be avoided.
I recommend that you speak to a patent attorney about your invention.
The second part, name protection, is a trademark issue. You're probably not close enough to getting to market to worry too much about trademark protection, but it's not a bad idea to think of some names and see if those domains are available. Your patent attorney will also likely be able to discuss trademarks with you.