We Volunteers cannot even begin to help until your post an active link to the blog in question starting with http://
You do not have to set up your comments up to accept "anonymous" commenting. Doing so opens your blog to auto-posting of comments made by trolls like the one your are experiencing as well as spammers. Go here > Settings > Discussion and set up comment Moderation.
There is a persistent and unsubstantiated belief that we each have individual IPs and they never change. That's nonsensical. In fact ISPs place hundreds of users in the same IP block to save money. Quite aside from that some have dynamic IPs that continually change. And any of us can easily get a new IP so IP blocking is not effective as a means to dealing with trolls.Moderating comments is. However, if you wish you can use the Comment Blacklist on the Settings > Discussion page.
When a comment contains any of these words in its content, name, URL, e-mail, or IP, it will be marked as spam. One word or IP per line. It will match inside words, so “press” will match “WordPress”.