How can I check available domain name?

You can also check domain availability at any web hosting site. If you do this, you can kill 2 birds with one stone. Check and purchase. I've used GoDaddy.com. The people are very good to work with and will help you 24 hours a day, if you need assistance for anything. Best Wishes!

go to godaddy and do a search there or just type the name in your browser if you get and error its free

You can check a domain name online. All you have to do is make a little change in the address and see if the new name is available. There is no way to check available names unless you type something in and check it.

I would go into godaddy.com or another site like that and type in the domain name you want without the extension. It will list the extensions that are available or make a suggestion of something similar.

You could just try googling each specific url that you like as that should either bring up a site or nothing. But a more accurate way is to go to a domain name/web hosting company and search using their site. I have usually done this on GoDaddy in the past but I am advising people to avoid this business now to protest the company owner's cruelty to animals.

May be it means that it is the name accepted, it does not mean that people use it, it may mean the name you gave can be used. I may be wrong, find out first. I do not think that will go on like this.

There are several sites that can help you. Most of these are cancelled domain names but they are for sale. Here is one such site: http://availabledomainnames.com/ You can still think of some unique name so that you do not have to buy the domain name.