1. Make sure you will choose the domain name related to your site. That is if you would like to create the site related to games then from it's name, end-user should get the purpose of the site.
2. Make sure to choose the domain extension carefully, If you are developing the educational site then the extension should be .edu so it will clarify the use of your website.
3. You can use country specific extensions too.
4. Use the top rated keywords while assigning name to your website so it will help you to rank your website in SEO
5. Domain name should be short and sweet, easy to remember. It should be easy to remember and catchy. I would suggest it should not be more than 20 o 25 characters. Because visitor should remember the name of your website easily. If it's too lengthy then no one remember it and as a result, no visitors, no money. Make sure it convey the purpose of your website.
Domain name popularity depends on factors like visitors, alexa, design, architecture, contents on the website , images and number of links pointing to your website, social site linking. You will need to review the all links connected to your website. You should remove the bad links that is spam links. Internal linking should be proper.
Hope this will help you.