Translation:Please write your name on the envelope.
The default order for comprehending Japanese sentences is first person, second person, third person, i. e., speaker, person addressed (you), someone else. Here, the speaker is telling you to do something, it is to be taken as your name unless he specifies someone else. In Japanese generally, what does not need to be said is not said but there are conventional ways of knowing what is not overtly expressed. (Verbum sap. sat.)