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.
Thanks for your response.
I am using the default template for all other pages, and have created a custom home page.
What would my single posts base need to be named?
You would name it
base-single.php, assuming you want it to apply to both built-in WordPress posts and any custom post types you may also register.
I always keep this post on the WordPress and Roots hierarchy handy.