Q. Does your domain name impact your SERPS (search engine results placement)? That is,if you use a nonsense name, will it negatively impact your search engine ranking? Would "www.thebestsearchengine.com" rank better than "www.google.com" for the query "best search engine"?
Ans: There are hundreds of different variables that modern search engines consider when determining which of the thousands - or millions - of results should be presented in the top slots, one of which is definitely the domain name of the site. Other variables include the age of the domain registration, the last time the DNS record was changed, how recently the page was changed, how many other pages point to the page in question, how those other pages link to the page, whether the words in question appear in the title of the page, in a header, how frequently the key word or words appear in the text, and on and on and on.
Indeed, we don't actually know the exact formula and there's an entire industry of people trying their very best to figure it out and then remarket the specific tactics and layout suggested by their experimental data (and guesses). They're Search Engine Optimizer (SEO) specialists and while some of them are sharp marketing professionals, many are snake-oil salesmen and should be avoided at all costs.
Back to your question, though!
Do a search on Google and you'll notice that in addition to matching words in the brief description, Google will also often highlight the portion of the domain name that matches too.
As a general comment, though, I'll say that my best advice to you is to focus on building the best possible content for your site, update it with some frequency, generously link to other relevant sites, and use some basic search engine SEO tactics without crossing the line into "black hat" or other dangerous and unethical tricks, and you'll do well in the search results. Focus on findability. and good luck to you .. Rishil