User identification associated with comments/replies

I have created a new blog using WordPress and, since I am new to blogging, do not understand how comments/replies work. Currently, an invited user is able to comment on any of my postings without individually registering with WordPress. Their comment/reply appears with my username as the author of their comment or reply! Therefore, it looks like I am writing my own comments/replies. How can I adjust the blog so that comments/replies from other people display with there own username, or alternatively, with their email address?