I'm not sure if I want to use real people and companies or make up an entirely different world with different people, presidents, and companies than our real world. If I did the latter I would offer the possibility of other universes in the preface and then use completely fictitious people. My main characters are of course fictitious, but they will be going on a journey to uncover hidden secrets from our nation's past and even from the world's past, so I need to know if these secrets they uncover can be about real people and companies (written in our real world) or if it would be better to make up companies and similar secrets to satisfy the story(written in an alternate universe).
The name of historical people or places is public domain(Our history is a shared one after all!) and no harm comes from involving any aspect of history in published fiction.
Having said that, using real companies(or their products) who have trademarks and copyrights will run you into complications that might just be best to avoid all together. If you are truly curious about the details, then this article and the blog it is from might be of help to you:
There are two potential categories of issues to using real people and organizations in a fiction story: legal and literary.
On the legal side, let me give the standard disclaimer, I am not a lawyer.
Casual references are no problem. Authors are always writing, "Bob drank a Coke" or "The old Ford had broken down again." Occasionally companies get picky about trademarks. Like writers have gotten letters from the Coca-Cola Company's lawyers because they wrote "coke" with a small "c" rather than a capital.
But I think you run into the risk of being sued for libel if you attribute illegal or scandalous behavior to real people and organizations. If you write a story in which you describe a real company as paying bribes or covering up accidental deaths in the factory or whatever, and you name specific, real officers in the company, they might well sue you for libel. Whether they would win depends on the specific details of what you said and how it was presented, not to mention the opinions of the judge and jury. But unless your goal is to paint people or organizations that you dislike as evil, you are taking a lot of risk for no apparent gain. If your goal is to say that this is the sort of behavior that you think these folks engage in or are likely to engage in, then be prepared to face the repercussions. If you end up in court, even if you win you could be out a lot of money for lawyers, etc.
The courts generally consider political figures to be "fair game". I recall a few years ago someone made a pornographic movie about a female politician that he didn't like in which he portrayed her as having sexual relations with pretty much every man she met, in which he openly used her name in the title of the movie and got an actress made up to look just like her, and I don't think it ever even went to court. I'm sure she knew she would lose and all she would accomplish would be to give free publicity to the movie.
From a literary point of view: Putting in casual background references to real people, places, companies, etc, can add to the realism of a story. It creates the catch that if you use real details, you should go to the effort to make them right. Like if you say, "Bob drove a 1967 pickup truck", no one's going to question it. But if you say, "Bob drove a 1967 Studebaker pickup", a reader might have trouble with that if he happens to know that Studebaker went out of business in 1966. (I've had times when I've noticed mistakes like that in a story and I've wondered if the WRITER made a mistake or if the CHARACTER made a mistake and this turns out to be a crucial clue to the identity of the criminal or some such.) Also, if you overdo it, it can make your story sound like one long commercial.
Using real people, etc, in a story where they are clearly presented as heroes or villains can limit your readership. If you present, say, the Catholic Church as a corrupt institution made up of superstitious lunatics, your book may be a hit among atheists but will likely be a hard sell to Catholics. You might manage to get your book categorized as "controversial" so that the people you attack feel obligated to read it so they can offer rebuttals. But for the most part that's a long shot -- only one novel every few years really makes a success out of being controversial. Books that offend a large percentage of the potential market tend to just not be read, because most people will say, Why should I give this person money to deliberately insult me? Again, if your goal is to attack some person or group you dislike, then that changes the equation, then you have to figure out how to do it most effectively. But if you're just trying to write an entertaining adventure yarn, painting some group as the villains when millions of potential readers are members or at least respect them, is just sabotaging yourself.
Legally, Presidents are largely free game. Largely.
You run a serious legal risk using real companies.
I love alternate history, this is where you take a historical account and change something, aliens invade during world war two, I travel back in time to kill my grandfather, etc.
There are specific rules to handling historical characters, firstly they aren't your character, be true to their known character. If you change a historical character you must have a good and obvious reason for the change that is clearly explained. Companies are built of people If you change a company you must either change the regulatory environment first, or change which people or change a historical character subject to the above guidelines, otherwise the company is not your character, be as accurate as possible. when in doubt let the company or historical character be great whether it be like taco bell in demolition man or like Sampson as he died.
If a historical character won't do what you want, kill him, all dead men are heroes or mayrters and the guy who took over can be your own creation.
Although these rules may not fit what you are doing exactly I still think they may be of help.