You can use a
mod_alias redirect. If using Apache 2.2.6+ then:
Redirect 301 /blog-domain-name /blog
/blog-domain-name is appended onto the end of the destination URL, no wildcard is necessary.
On earlier versions of Apache you will need to specify an absolute destination URL:
Redirect 301 /blog-domain-name http://example.com/blog
Will new blog URL know that I want all requests arriving at destination blog posts?
Not sure what you mean by this? Isn't the "new blog URL" the "destination blog"? The "new blog URL" won't know whether the request has been redirected or not.
UPDATE: From comments, it seems that the actual requirement is to change the URL structure. The "new blog name" (ie. the destination URL) does not currently exist and results in a 404. A simple 301 redirect is therefore not appropriate in this instance.