Hazing, rudeness and bad manners are not illegal, generally.
If the sign doesn't violate zoning ordinances, there is no nuisance in such cases.
In similar type situations, one neighbor might approach the other (or write a polite letter) and explain that the sign and the nickname are offensive. If that's not practical, most would counsel that the neighbors be ignored.
The information provided here should not be construed to be formal legal advice. The provision of this general advice does not create a lawyer-client relationship. Persons with legal questions are encouraged to seek independent counsel for advice regarding their individual legal issues.