In the last couple weeks, Google’s mobile search results updated to display site names.
If non-optimized, you’ll see the domain name instead, so for example, rdldigital.com instead of RDLDIGITAL.
While Google relies automatically on titles, Open Graph Protocol site_names & headers to create them, you can be explicit through WebSite structured data on your homepage.
An established SEO best practice that should now change is to stop appending your brand to title tags!
This now wastes valuable characters before truncation of the title in search results (~65 characters). You could include more keywords to be more specific, or often more importantly, something compelling like provoking curiosity, including a call-to-action, and so forth.
This is even more true since this will eventually roll out to desktop.
SEO constantly evolves. For a midsize or larger business, with enough search intent & web content, these small optimizations add up to provide a competitive advantage. This means more keyword rankings, traffic & revenue from organic search in the long run.