It may be possible to do that, but exactly how, I’m not sure. It’s a permalink setting that would fall outside the default options. For pages and posts when you choose the post name option, it leaves out “page” or “post” from the URL slug. With a custom post type, the post name permalink option will add a slug to it. That’s why you’ll see a staff person’s url be /staff/name instead of just /name.
When you register a custom post type you can change that, but I don’t know if you can first add the post type slug to the permalinks for page and posts and secondly if you can change it to “blog” from posts.
You can probably find the answer via Google, but it’s going to take some digging just due to the sheer volume of items out there related to permalinks and WordPress.
If it exists, it’ll be something you can add via a site specific plugin or the theme’s functions.php file.