(1) After the entry of an order of adoption, if the adoptee‘s name is changed, the adoptee shall be known and called by the new name. The person or persons adopting the adoptee then become the parent or parents of the adoptee under the law as though the adopted person had been born to the adopting parents and are liable for all the duties and entitled to all the rights of parents.

  (2) After entry of the order of adoption, there is no distinction between the rights and duties of natural progeny and adopted persons, and the adopted person becomes an heir at law of the adopting parent or parents and an heir at law of the lineal and collateral kindred of the adopting parent or parents. After entry of the order of adoption, except as provided in section 2114(2) of the estates and protected individuals code, 1998 PA 386, MCL 700.2114, an adopted child is no longer an heir at law of a parent whose rights have been terminated under this chapter or chapter XIIA or the lineal or collateral kindred of that parent, nor is an adopted adult an heir at law of a person who was his or her parent at the time the order of adoption was entered or the lineal or collateral kindred of that person, except that a right, title, or interest that has vested before entry of the final order of adoption is not divested by that order.

  (3) This section does not prohibit the filing of an action or entry of an order for grandparenting time as provided in section 7b of the child custody act of 1970, 1970 PA 91, MCL 722.27b.