Can Someone Find Me with My IP Address?
No. Mostly, people can only determine who your ISP is, state and city that your ISP resides in; but not your home address.
Yes. If the law comes in, they can find you through your ISP.
How can someone find out who I am?
If someone knows your IP address, they can do a lookup on your ISP and they will know only the physical location of your ISP, but not your home address.
But if the law comes in, a court can order the ISP to reveal who is using certain IP address on a certain date and time. And the ISP knows where their subscriber’s home address is.
In conclusion, if you want high level of anonymity, you may read more about Internet Anonymity, Proxy Servers and how to hide your IP address.