User Causing Emotional Stress

I have a person who keeps making a name on my forum even though I banned their IP. Either they're reseting their IP or there's another reason. Each time the IP is increased by one number which is why I believe they're reseting it. They continue to upset the other users in the Chatbox. I was one of the upset users. I continue to delete their names and ban them but they keep making a new name anyway.

I'm at a loss for what to do now. Anyone have an answer?

They are using a proxy to get around the ban. So banning the IP won't work with proxies. I don't know of a way to stop them if they are using a proxy Other than contacting their ISP(Harassment), that might be the only way. Are they using the same email?

If they are just making slight changes in their IP you can range ban them.
Go to acp > users group > Ban an IP address & install the IP like so.
For example made up IP. 72.222.54.12 replace the last series of numbers with an * like so 72.222.54.* if need be strengthen it like so 72.222.*.*
If they are using a proxy theres not a lot you can do about it just keep banning em.

Orthodox moderation technique says that you simply keep banning them until they get bored and realize that they have no life.

Unorthodox moderation suggests that you simply use a wild card on the IP ban for a while (banning all IP addresses of a region) until you believe its safe to lift the ban an allow other users of that region to register. This should force the pest to give up and move on.