Right...I'm going to put on my publisher hat now, and hopefully clarify a couple of issues...
(For the record, I am a publisher and author, not a lawyer, and this should not be taken as legal advice.)
There are two main forms of intellectual property at play in something like this: trademark and copyright.
Copyright is by far the more common, and it is created as soon as a work is put into a fixed state, meaning that once a character you have created exists on the page, you own that character. This copyright exists for your lifetime plus 50 or more years, depending on the country (Canada is 50 years, much of Europe and the United States is 70 years). And, copyright is mainly based on implementation of an idea.
So, for example, I have a registered copyright for Re:Apotheosis, which means that mech pilot Major Atria Silversword and her mech Volundpanzer are my intellectual property - if somebody uses them without my permission, I can take legal action against them. However, if you create magical knight Lady Atria Silversword who has an entirely different backstory, attributes, and character arc, I probably won't like the fact that you scooped the name, but there is nothing I can do about it - Lady Atria Silversword is NOT Major Atria Silversword, and belongs to you.
A trademark, on the other hand, is very different. A trademark is generally used for a product name, but it is also used for characters such as superheroes. A trademark allows one to protect not just the implementation of an idea (such as Superman), but the name as well. The reasoning is that the owner of a trademark has to prevent confusion and prevent the dilution of the brand. Further, a trademark can be declared invalid if it is not protected by the rights holder - this means that if you decide to publish a story involving a superhero named Superman, there is a very serious incentive for DC to take legal action against you, even if your Superman doesn't have any resemblance to theirs other than the name.
There is a limitation on this, however: you cannot trademark commonly used words (or, at least, such a trademark won't survive a legal challenge). So, Superman can be a trademark, and Mickey Mouse can be a trademark, but not House. Yes, you can have a character named Dr. Gregory House, but you cannot trademark that name and try to prevent others from using the word "House" in their company names or products. Microsoft got into a lot of trouble trying to enforce a trademark on Windows, and nearly had it invalidated on grounds of being too generic a word for trademarking (they avoided this by settling the suit - you can read about it at https://en.wikipedia.org/wiki/Microsoft_Corp._v._Lindows.com,_Inc.).
So, if a character is protected by copyright, you're not in any danger if you accidentally copy the name of that character. If a character is protected by trademark, unless that name is VERY generic and you can prove that lots of other characters have used that name in the past before the trademark existed, you can have a reasonable expectation of legal action being taken once the trademark owner notices what you are doing.
Or, put another way, if the name is trademarked, it's safer to just pick another.