Know the name of someone who traced your IP? The record of IP Addresses is (basically) a public database. Tracing IP's doesn't necessarily require registration, so there may not be a way to find that out. Now, matching an IP to a name is usually a different matter. Most privacy laws require court approval to do that.
There are some crazy situations where that's done in secret, but the court action, if done, is also a public record. So you might be able to find the person that way. Generally, you want a legal professional to help you with that.