Upon death of the last living Trustor, the Trust itself becomes an Irrevocable Trust, but the name remains Living Trust as no changes to the Trust can be made. 

Under the demographics of the Trust, the “Account Type” will change from “Trust” to “Irrevocable Trust” but the name stays the same.

Taking checks made payable to the “Irrevocable Trust” are then grey area management as it's technically made payable to the type of entity, not the actual name of the Trust.