How can I determine whether I can use a name commercially? Where can I search for whether I can or cannot use the name "Connect 4" or "Connect four" for my game?
In the United States you can search trademarks at the U.S. Patent and Trademark Office (USPTO) website. http://www.uspto.gov/trademarks-application-process/search-trademark-database
A bankrupt company's assets are transferred to its creditors. This includes intangible assets such as trademarks, copyrights, and other intellectual property. Whoever ends up with the rights to the game can continue to market and distribute it, or use legal means to prevent others from doing so.
As you have agreed, by contract, not to reverse engineer the product, technically it would be a "breach of contract" to do so, assuming such terms are enforceable where you live (or wherever the EULA selects as the choice of forum).
The most important fact to bear in mind is that there's no way to predict whether a given individual will decide to file a suit against you, though we might say on what basis he might, if he so chooses. There are two basic grounds for a suit, one pertaining to trademarks and the other pertaining to use of names – misappropriation and violating the right of publicity. A word can be a trademark, but the scope of protection is somewhat narrow because the protection is in terms of use within a given business. So calling your computer company "Apple" is out, but calling you roofing service the same is okay (assuming that somebody didn't previously register "Apple Roofing"). The main consideration is the likelihood of confusion. Supposing your business were selling landline telephones and I don't think Apple computer company sells such phones, you might still be in trouble if you called your company "Apple Phone", since they certainly do sell phones. There are thousands of trademarks that include "Puff", including Cocopuffs and various pizza and cheese puffs. Since "Puff" is such a generic word, there is a higher bar to proving infringement (there are thousands of trademarks including "Puff"). "Puff Daddy" is, however, a registered trademark covering perfume, jewelry, clothing and certain online services, so there is a non-negligible chance of confusion. In the case of names (or apparent names), an additional concern is whether this is commercial exploitation without consent of a person's name (which causes harm to the subject). The underpinning of this tort is that such a use falsely implies an endorsement of the product. Again, with a fairly generic word like Puff, there isn't a clear implication that Sean Combs has endorsed a product that is called "Puff Communications", but "Puff Daddy Communications" would almost certainly cross that line. The main issues, then, are the extent to which the name is generic vs. unique, and whether it is likely that a person would interpret the product or service as being the same as another, or would constitute an endorsement.
It is not clear to me how you &quot;use&quot; a mythological entity, and I take no position as to the divine consequences of any unauthorized uses, but you are entitled to incorporate then in your own intellectual creations for two reasons. First, any imaginable copyright on original texts (e.g. the Bhagavad Gita) has long since expired. Not all texts are of such certifiably ancient provenance, so there may be contemporary texts created by a practitioner of Ásatrúarfélagið which is protected. Second, names (Amitāyus, Zaraθuštra, Ngai) are not protected by copyright, so you can use names.
It's best to use formal names in legal documents. For example, Ringo Starr's musical compositions are credited to Richard Starkey. If you have a business that wishes to do business under a name other than its legal name, you can investigate d/b/a (&quot;doing business as&quot;) designation. For the purpose of a single contract or other document, you can usually include language that designates a name for the business such as &quot;this agreement is between Full Name Incorporation, Inc, hereinafter known as Trademark®, and....&quot; You shouldn't do any of this in real life, however, without first discussing it with your lawyer. If you believe that there is business value in calling your company &quot;Foo&quot; when its actual name is &quot;Bar Corp,&quot; then surely that value warrants some expense to find a lawyer who will defend the validity of the company's contracts in court, should that become necessary.
There are several things going on with Akinator and their use of trademarked names and characters. If you look at akinator.com Legal Notices it says: 2 – Copyright – Reproduction rights All the content of this site falls under French and international legislation on copyright and intellectual property. All rights reserved. Reproduction in whole or in part of this website, in any form or by any means is strictly prohibited without prior authorisation of the publications director. All products and trademarks mentioned are property of their respective owners. (emphasis mine) The fact that they mention that all trademarks belong to their respective owners is good, but it's a formality. What it appears the site really relies on for use of trademarked characters is what's called Nominative Use, which is a type of "trademark fair use." The product or service cannot be readily identified without using the trademark (e.g. trademark is descriptive of a person, place, or product attribute). https://en.wikipedia.org/wiki/Nominative_use Akinator has to use the names and trademarks to identify those names and trademarks. Akinator could possibly be sued to establish their type of fair use is not valid in their case, but it's probably not worth it for the companies to pursue. And, most companies would rather people use and see their trademarks in a marketing and money-making fair use sense rather than sue to stop their use. See In the US, when is fair use a defense to copyright infringement? for a full description of Fair Use. Now, when you get to the "answer" part of the game, you will see a "copyright" link. Part of that resulting page says Displayed pictures are accessible from the web. It is Elokence's policy to respond to notices of alleged copyright infringement that comply with applicable international intellectual property law and make the necessary changes. In respect of Elokence's Intellectual Property Policy, Elokence operates a complaints procedure accessible via the form below. So the company has given itself a further bit of protection by only using images on the web they can link to (at least in the web browser game; I don't know about the App), so that means the image is already "out there", uploaded by someone else, and Akinator can claim they didn't upload it. And, further, there is a contact form for trademark holders to send DMCA takedown notices for their work. It's a belt and suspenders approach to the use of trademarks in their game.
Names of people, institutions, and events are not protected by copyright. Things that have occurred at events like math tournaments are facts, and may be recounted, in your own words, with no fear of infringing any copyright. Facts are never protected by copyright, although a particular description of facts could be, and so could a particular selection and arrangement of facts. Specific math techniques and their names are not protected either, and may be described without infringing copyright. The items you mention in the question are: video game / movie references and names No copyright issue here. common integration bee problems No copyright issue here. names of a university / math competition organizers No copyright issue here. integration techniques and formulas No copyright issue here, unless you copy an extensive description of a technique without rewriting it in your mown words.. using someone's Overleaf Latex package to format the book This depends on the license for the package, but there is not likely to be an issue. In short I think you are worrying over issues that are in fact non-issues.