Process serving is not a terribly dangerous job. Yes, there are occasions when emotionally unstable people want to take out their frustrations on the messenger, but even then, a process server can usually diffuse those situations by remaining courteous and leaving quickly.
Movies and TV shows, even a certain "reality" show I saw a few years ago, portray people receiving court papers as angry and argumentative, running away, or throwing things at the person trying to serve the papers. In fact, most people receiving court papers do accept service respectfully and without incident.
A person who delivers court documents does not need to physically touch anybody with the papers. There is no need to announce, "You've been served!" And there's no need to carry a badge, although in some states the law allows process servers the option and there are some who like having one. As for making a serve, it's standard practice to simply mention the general nature of the documents and leave them nearby if the person refuses to take them in hand. If they have any questions about the documents, the server should keep comments brief and refer them to any contact numbers on the documents.
False portrayals of process serving on TV and movies show process servers chasing down "bad" people and defending themselves from big, angry characters. This doesn't help the public's perception of process serving, nor the perception some process servers have of themselves. Process servers are not law enforcement officials, even if they choose to carry a badge.
Personally, I've had a few people try to argue with me when I serve them court documents. Assault on a registered process server is actually a felony, but I'm not about hang around just to remind anybody of that and dare them to make a move. The key is to be respectful and courteous, not aggressive and confrontational, make the service, and leave. And that's what most people who serve legal documents actually do.