Using the name wiki in my domain name ? Legal ? Copyright problems?

I would like to use the word wiki in my domain name, such as fastbikiwiki.com

Is this legal or because of wikipedia, it would be a copyright issue using wiki in my domain name ?

For a legal answer, you should consult an attorney that practices in your jurisdiction.

Trademarks can exists in two ways, common law trademarks and registered trademarks. You can easily inquire from the trademark office (most have a search option on their website) if wiki is a registered trademark. If so you can also see for which industries it is trademarked. If you are outside, you should be fine with that.

However, it is not necessary to register a trademark in order to have one. There is also something that is called common law trademark. This makes it usually a little more complicated.

However, it is also important to understand, that the trademark name cannot be an object of what you sell. If you are a fruit and vegetable trader, you usually cannot trademark the term apple. However, if the object is irrelevant to your business you can (i.e. the beatles trademarked apple for the music industry, Apple Computers for the IT industry).

As broader a term is used in a certain context, as more difficult it is often to trademark it. Since wikis already existed before wikimedia, and without doing a search, my feeling would say, that you probably would not have too many issues with your domain name. However, in order to be safe, consult an attorney.

In regards to copyright. Single words or small phrases cannot infringe copyright. Most copyright legislation is quite explicit that in order to copyright something it must be a work of creation. One or two words do not really fall into this category. However, again, if in doubt get legal advice from an attorney.

Wikipedia was not the first wiki, and there are already other companies with "wiki" in the title. In terms of legality / trademarking, you don't have a problem.