Can an executor sign legal documents by simply signing their own name or does it have to also say Executor for the estate of so-and-so?

An Executor signing a legal document for an Estate must include "Executor, Estate of...." Also, as Executor, you may have to request various information (non legal)in writing, and must include Executor, Estate of with your signature. Some info may require proof of your appointment as executor in the form of Letters of Testamentary. Some may also require including a copy of the Death Certificate.