An irrevocable trust owner typically can't change the trust's terms or end the agreement. A trust's owner may name a beneficiary—a person who receives income and assets from the trust—as trustee or successor trustee in the agreement.or example, an agreement might allow trustee removal only if all beneficiaries and the trustor agree. Other than age requirements—trustees must be at least 18 years of age—state laws don't restrict a trustor's trustee choice, so the trustor may name a beneficiary as trustee or alternate trustee.