With regards to the premise of your question, there are other agencies that use "US," including the USPS (postal service), USGS (geologic survey), USDA (dept of agriculture), USMC (marine corps), and the USFS (forest service). So they're not as exceptional as you may have thought.

As far back as the incorporation of the Service Star in the official badge in 1875, it has read "US Secret Service," with "Secret" and "Service" arcing around a central "US".

That would suggest that, at least officially, the Secret Service was never just called "SS".

The US Secret Service seems to be the only federal agency that incorporates "United States" in their acronym.

On it's face, this is totally inaccurate. In fact, there are any number of federal agencies that incorporate "United States" in ther acronym. I don't even know where to begin; USFS, USPS, USFDA, USMC, ad nauseum.

Presumably, they do this to avoid being called the "SS."

I don't think so. To my mind you are begging the question in the traditional sense of the term by asking us to accept your proposition as a given, when in fact, there is no real reason to do so.

As a direct rebuttal of your supposition I would raise the term USS --a designation meaning "United States Ship,"-- that has existed since the dawn of the nation and that, far from having anything at all to do with Nazis, was meant to differentiate US ships from the HMS --"his/her majesty's ship-- of the British Empire.

Christ. I am drunk and tired and should go to bed. I'm not at all sure that any of the above actually makes sense.

I know of at least one case of the Secret Service being referred to as the "S.S." in a noteworthy context.

On November 1, 1950, two Puerto Rican nationalists attempted to assassinate President Harry S. Truman at Blair House in Washington. White House Police* Officer Leslie Coffelt was killed in the gunfire, to date the only Secret Service agent or officer ever murdered protecting the President. In a letter four days later, Truman wrote (emphases added):

Because two crackpots or crazy men tried to shoot me a few days ago my good and efficient guards are nervous. So I'm trying to be as helpful as I can. Would like very much to take a walk this morning but the S.S. say that there are more crackpots around and the "Boss" and Margie are worried about me—so I won't take my usual walk.

And then again on the 17th:

I've always thought that if I could get my hands on a would-be assassin he'd never try it again. But I guess that's impossible. The grand guards who were hurt in the attempt on me didn't have a fair chance. The one who was killed was just cold bloodedly murdered before he could do anything. But his assassin did not live but a couple of minutes – one of the S.S. men put a bullet in one ear and it came out the other. I stuck my head out the upstairs window to see what was going on. One of the guards yelled "Get back." I did, then dressed and went down stairs. I was the only calm one in the house. You see I've been shot at by experts and unless your name's on the bullet you needn't be afraid—and that of course you can't find out, so why worry.

The S.S. chief said to me, "Mr. President, don't you know that when there's an Air Raid Alarm you don't run out and look up, you go for cover." I saw the point but it was over then.

(Source.)

That said, I have no idea how common such an abbreviation was at the time. It could have been entirely idiosyncratic to Truman. Perhaps someone else can provide more clarity on that matter. But it is nonetheless interesting that five years after World War II, "S.S." was being used to refer to the Secret Service by no less than the President of the United States.

^(*The White House Police, despite sounding like a separate agency, were part of the Secret Service. They're now known as the Secret Service Uniformed Division.)

I apologize in advance that this isn't going to have sources, so delete away if needed. But there is Norman Rockwell painting/illustration hanging in the entrance lobby of the West Wing at the White House. It's called "Waiting to see the President" or something like that. On it, one of the men is labeled "S.S. man".

I've been told this painting/illustration was done directly for the White House and there is no known photo or print of it. A quick search of the internets seems to confirm this, but perhaps others have better google-fu or art history knowledge than me (I found what appears to be a partial of the larger piece Rockwell seemingly did for a magazine).

So sorry I can't cite a source other than my own eyes, but it's there.