can my ex wife and son move in with her new boyfriend without me knowing the boyfriend?

There is no law on the books that prevents the Mother and your son from moving in with anybody she wishes. Same applies to you. However, you do have the right to know who your son lives with and should be provided with the boyfriend's name. The only way this situation can become "actionable" is if the boyfriend's criminal history, other habits, and/or behavior towards your son makes it that it is not in your child's best interest to be around him. Then you can file to modify the timesharing arrangement, if the Mother insists on living with the boyfriend. After you find out his name, I suggest you run a background check on him. Best of Luck, Helena Y. Farber, Esq. ~Associate Attorney~ Law Office of Cindy S. Vova, P.A.   www.vovalaw.com