If I understand your request correctly, it sounds like you want to add some text to the right of the site title or logo. There are many ways to do it, but I would recommend using the site tagline option available in the Customizer. By default, the tagline appears below the logo, which does not meet your expectations.
However, it is possible to use CSS to “float” the site title (logo) to the left. This allows the tagline to appear on the right side of the site title or logo.
This is the HTML output:
<h1 class=”site-title” style=” float: left;”><a href=”http://example.com” rel=”home”>Site Title</a></h1>
In CSS, it would look like something like this:
.site-title {
float: left
}
Once the title (logo) is floated along the left side, you can style the tagline according to your own needs. The exact spacing is determined by your unqiue preference.
The custom CSS editors are really good for quick fixes or testing, but for a significant rearranging the of the layout of the theme, a more permanent solution would be ideal. In which case, the best and safest way to make these changes is in a BoldGrid child theme.