I am using Roots and need my blog and blog post pages to use a different template than the rest of my site.
I recognize that the single.php and content-single.php are displaying the content.
Do I need a new base-*.php file to control these and if so does this need a specific name?
No, you do not need to create a new base template. You would only want to create a custom base template for your home page and your single posts if you need to customize the markup contained within the default base template for just those two templates while using the default base template for all other pages.