Recently, Google has been replacing many domains in SERPs with website titles, e.g. "Stack Exchange" instead of "stackexchange.com".
However many smaller sites, including my own, only show a URL and not a "website title":
What is this feature called in Google Search, and how can one affect it from an SEO standpoint?
Those are a kind of google experiment. Some of them run in a limited environment and for a small selected number of websites, and when they intend to implement it widely, you will see it affecting even your website.
As far as its effect on SEO, I don't think it has any effect unless you have an appealing website name that might increase your site's SERP ctr, other than that it is just google experimenting, trying to visually improve its search result pages.
