How would one write in an adopted child as a beneficiary of a trust

A trust can be of different forms, generally though, a living trust, often used, operates during the lifetime of it's creator (you), to entrust property management to the 'trustee' who manages assets. Trusts are used primarily to avoid probate as you probably know, and they remain private while a will becomes public information after the testator dies. Also while they are more expensive to draft , they save some money in the long run. At the inception of the trust it is managed by the creator. Trusts are revocable or irrevocable, changeable by creator or not changeable. When the creator becomes disabled the trustee takes over management in either, but if revocable the creator can alter or amend trust at any time. If the creator dies the trustee then can distribute the assets to beneficiaries as he chooses. So if your son were to decide to make his wife or adopted daughter beneficiary he would be free to do so. If you want another arrangement have your paralegal/attorney amend the trust if it's revocable. It is a major decision not without complications & only you can make it without any ambiguity or interference.