Note: We strongly recommend using a child theme if you are planning on modifying theme template files like the header.php so your changes are not overwritten when you update your theme. You can learn about how to create a child theme to retain your customizations here.
By default Divi only displays the logo image on your site, if you want to add a text below the logo, some sort of sub-heading, then follow these instructions:
1- Open the header.php file of your theme. (Use FTP, cPanel’s file manager or from within dashboard => Appearance => Editor).
2- Search for this line:
<img src="<?php echo esc_attr( $logo ); ?>" alt="<?php echo esc_attr( get_bloginfo( 'name' ) ); ?>" id="logo" data-height-percentage="<?php echo esc_attr( et_get_option( 'logo_height', '54' ) ); ?>" />
3- Add right after it this code:
<p class="cu-sub-title"><?php echo esc_attr( get_bloginfo( 'description' ) ); ?>
Now you will see the subèheading of your website under the logo, there could be some positioning issues though, depending on the layouts of your header, the following code might and might not help but you can try it. Please add this code in Divi => Theme Options => Custom CSS:
If things look good to you, then move the header.php file to the child theme folder so you can retain this change when you update.
If you are new to creating a child theme, you can checkout our guide here.