If your company is called "Liam's Company" and your main website is at "liamscompany.com" then you can put the blog either at "liamscompany.com/blog" or "blog.liamscompany.com".
Personally, I prefer the former, because it tends to have fewer technical issues, but the latter also works (especially now that Google recognises the link between the different subdomains).
The problem with liamscompanyblog.com is that it really makes things confusing for:
- Marketing - do you point users to liamscompany.com or liamscompanyblog.com or both?
- SEO - you are now trying to get backlinks for two sites, so both sites will have less value rather both being added together
- Reputation - a lot of fake sites exist with a real company name and blog just appended on the end. You have to spend unnecessary time establishing that this is a real blog.
- Technical - with two domains, you start to get issues like browsers blocking requests between two domains (to prevent XSS attacks), cookies (making your web analytics less reliable)
- Legal - does somebody who opts-in on liamscompanyblog.com has registered to receive email from liamscompany.com?
It's possible to get round these issues, but why bother spending your time on this when you could be writing great content.
There are only 2 reasons I can think of why you wouldn't do this:
- If your blog is not 100% representative of what you do. For example, if you are a clothes company, but your blog talks a lot about the technical difficulties of running a clothes website, Google is going to be confused as to what your website is about so you could get sandboxed.
- Your blog is about the person rather than the company, with personal opinions and content that are not necessarily company related. This is partly an extension of #1 (if the CEO of a clothes company starts writing about his new car, that's going to look odd for Google). And partly because it separates things legally - these opinions are not representative of the company, etc. Plus, if your CEO leaves, he keeps his blog and it's not connected with you any more.