If a logo is used, it is recommended that the Google Sites Logo dialog box not be used. The logo will take up limited header space, moving the header title out of its way. There is less header title control using this method.
Instead, add the logo to the header image. Download the header image from the Downloads page, modify it and reupload it.
Or decrease the website name font size to allow both the logo and the font name to sit next to each other without affecting each other.