The default comment system uses the defined admin contact email for where to send moderation emails. For a single user blog that is fine, but for a company site one person or multiple persons may be dealing with comments. I have found no easy work around for that.
As a question on this,
What is easiest way, either function or plugin snippet or full plugin, to make it that the client (owner of the website) gets notification of comments etc. but no site admin emails and that I, as the website maintainer, get the site admin emails and not the client stuff.