Sorry if I butchered the title/question. Say my name is John Fernandes and my website is "johnfernand.es". If someone Googles "John Fernandes" will it match "johnfernand.es" like it would "twitter.com/johnfernandes"?
It is not necessary. Google and other Search Engines (SE) rank websites in the Search Engine Results Pages (SERP) based on their usability rating, in accordance to the SE's algorithm. Having said that you need to have content related to the domain name and the website hosted on this web address to be popular and to offer valuable information.