So I'm writing a book, (duh) and I want to include a mention of a Tim Hortons cup, (Canadian coffee place) just to hint at the reader that I'm Canadian. I want to put it in there casually; it's gonna be mentioned as empty. But I'm not sure if I need the copyright to Tim Hortons first or not. Can anyone help me out?
As @MonicaCellio noted in her comment, a name like "Tim Horton's" cannot be copyrighted. You can't copyright a name or slogan. It can have trademark protection, which is a different thing.
So to really answer your question: The point of trademark law is to prevent someone else from confusing potential customers of your product by using your name. Like if you tried to open your own coffee shop and call it "Tim Horton's", the existing Tim Horton's would have a very clear case for a trademark violation lawsuit.
But you are perfectly free to use the name "Tim Horton's" in speech or writing to refer to the real company. In general they're probably glad if you do -- free advertising.
Companies will bring law suits about mis-use of their trademark. Especially if you use a trademark as if it was a generic term, like Coca Cola is famous for suing people for using the word "coke" as a generic synonym for "cola". But I don't think that's the issue here. You're not referring to all Canadians as "hortons", I don't think.
There is the issue of libel if you say something bad about them. If you say that their coffee is contaminated with rat droppings or that the company paid bribes to politicians, they could sue you for libel. (In the US, if you can prove in court that your statements are true, you will win. I understand that truth is not an absolute defense against libel Britain and Australia, I don't know about Canada.)
But a simple casual reference like, "Bob dropped by a Tim Horton's and got a donut and a cup of coffee" is no problem at all.
You may write:
When he came down from the Empire State Building, where he had been surprised to find Donald Trump giving an interview, John picked up a cup of coffee at Starbucks and slowly ambled down the street, enjoying the feel of his new Converse sneakers. Just as he was about to get into his BMW, his iPhone rang and he saw that it was Joan from Microsoft, who he had met on Facebook after he had been dumped by that CIA chick from Tinder. "I used to think maybe you loved me now baby I'm sure", he hummed, as he swiped to answer the call.
Nothing in this passage is protected by copyright or trademark law, and since there is no slander, it is completely unproblematic to bring in existing persons, buildings, companies, or government agencies or even quote a verse from a pop song.
If, on the other hand, you plan to show how your protagonist got sick and almost died from the coffee and how it is uncovered that mismanagement, greed, and corruption have compromised the quality of industrial food, you better invent a company and make sure it does not remind anyone of one specific real franchise.
No, a casual mention of a coffee cup is not going to get you hit by the copy right police. You're not doing the brand any serious harm (heck, the fact that it's empty means someone really enjoyed to coffee) and if anything, they'll see it as free advertisement. I recall part of the fun of reading Animorphs as a kid was that they did make reference to a ton of actual chains, stores, and other products I was familiar with as a kid (On two separate occasions, two different alien races thought Star Trek was the real deal and were terrified because of it... until they learned it was a work of fiction.).
As long as you're not being too mean to the company, and even then, it's still an issue of fair use, since the company does make a product and criticism typically falls under that. In these cases, case law holds that the holder of the copyright must show that they have considered the case as Fair Use before moving forward with the suit (Youtube got into some trouble about a year and a half ago because they were blindly accepting copyright claims and disregarding Fair Use counter claims. See "Where's the Fair Use" or #wtfu.).
In the United States, there was a case that held that using a pop song snippet of a pop song in an independently made video is not a copyright violation of the song in question, so long as the video is a derivative in nature. Popular Parody Artist Weird Al famously asks for permission from a song artist if he wants to parody them, but it is out of respect for the artist as a creator, not because of any law. Since Canada and the United States are under Common Law, they same would hold true as Common Law nations may use case law from other nations under a Common Law system to interpret their own laws. Since the United States and Canada are both Constitutional Government (i.e. they have a strict lists of laws that cannot be superseded) as opposed to Nations like the UK, Australia, and New Zealand (which are parliamentary, i.e. Laws made by Parliament cannot be superseded) it should be a matter of looking for any fair use differences on a Constitutional level, so you don't need to get terribly deep into legal case work.
On a note about Slander/Libel, if you are a United States Resident/Citizen, the U.S. will not extradite someone to stand for Defamation Suits in other districts if they are not legally considered Defamation in the United States. Either way, United States Jurisprudence holds that the all speech is assumed to be Free Speech unless proven otherwise (that is, Speech is innocent until proven guilty)... And the US is considered one of the most (if not outright the most) liberal nations when it comes to Free Speech.
Near as I can tell, the major difference between Free Speech in the United States and Canada has little to do with Defimation or Copyright. The biggest gap is over laws banning Hate Speech (Canada does have them... the United States does not).