Length of the domain name has a little to do with the search engine result. If your site is widely used, and the content is appealing enough to catch people’s attention, it will automatically rank up in the search result.
However, the domain name should be such that it reflects the purpose of the site. Unique and an optimal length domain name work the best. A longer name might also be good if it stands out, but there is a chance for people to forget it.