The short answer? No.
Speaking from a U.S. perspective:
In order for anyone to file a complaint and recover a registered domain, you would have to knowingly register a trademark as a domain name. The term knowingly is a high standard to meet. The trademark owner has to prove that you intentionally and knowingly used a trademark. There are other considerations I will cover can effect your use of a trademark for a domain name.
A company name in of itself is not a trademark. A trademark has to be registered. I will get into company names in a bit.
Common dictionary terms cannot be a trademark. There are times where common words are registered as a trademark, however, this can be easily challenged and reversed based upon U.S. Trademark Law. This means the term elephant cannot be a trademark.
As well, any complaint would have to argue that confusion would exist between any trademark and use of a domain name. For example, how many companies exist using the name Luigi? Tons. Luigi is a common name and cannot be a trademark. However, Luigi's Pizza probably exists more times than we can count. Luigi's Pizza can be a trademark. Part of a trademark is the geographical limitation of the trademark. For example, a Luigi's Pizza in Philadelphia would be limited in scope and would not trample Luigi's Pizza trademark in New York.
As for company names that are not trademarked. Most of the same considerations apply without the legal protections of a registered trademark. The primary difference is that business names are local. For example, the name City Cellular in San Francisco not being a registered trademark would be limited to San Francisco and so a Boston company can register the name City Cellular giving that it is their business name without a worry.
On the web, the standard is extremely high for a complaint. For any domain to be taken away, the trademark has to be very well known and very large in scope such as Coke-Cola or it would have to be displayed that you knowing used and targeted a specific trademark.
Another consideration is your right to free speech. For example, how many domain names have a trademark name followed by the word sucks (forgive me SE)? This is your right to register the domain name. However, you can be sued in civil court and a demand to remove the domain name and site made. This is a different matter of course. This follows defamation and possible slander laws and not the use of the domain name itself. For a domain name of this type to be taken away, again, the use of the trademark has to be argued and it is not as common that these domain names are revoked. The primary argument for being able to retain the domain name is that the domain is clearly not representative of the trademark or intended to confuse the trademark. Of course this is not recommended.