Would renaming your SSID to “F.B.I. Joint Terrorism Task Force Surveillance Van” or something similar be considered impersonating a federal agent?
No, at least not in any jurisdiction I’m aware of.
While it’s unlikely that any statute anywhere has addressed the issue of impersonation via SSID directly, a required element of criminal impersonation charges generally is that the subject acts with intent to obtain a benefit, to injure another person, or to induce another person to submit to the pretended authority. Generally also required is that a direct claim to be a law enforcement officer, or display of an identifiable uniform or badge.
For example, NY Penal Law: Article 190 | New York State Penal Law | Frauds | NYS Laws
Anyway, when the intent is clearly to propagate a well-known joke, legal defense should be pretty easy.
No, but it would be considered engaging in an extremely old joke in the third degree.
An “extremely old” joke about wifi? This makes me feel old. 
That’s the equivalent of flashing a “Secret Agent” badge you can buy in a toy store.
So I can’t get in trouble if I tell women I’m a Feeling Boobs Inspector?
As long as you don’t interfere with the work of those who are actually charged with this task.
It’ll be more fun to call your router “Marijuana Grow House”. Then just kick back and watch the real surveillance vans gather 'round.
On a related note:
How does that compare to your “deflectoscreeching[sup]1[/sup]” neologism?
Awww FUCK!!!
<hands over a buck>
Could someone humor me and explain what the old joke being rehashed is? I’m ashamed to say it but I’ve never heard it before 
Step 1: Unsuspecting person in their home checks to see what Wi-fi networks are available.
Step 2: Person sees that the “FBI” has a network within range, supposedly within a van nearby.
Step 3: Person supposedly freaks out. No profit ensues.
Wow no wonder I’ve never heard of this “prank” or “joke.” That’s just stupid and lame. Is there really nothing more to it than that?
No, and it might help you to get it off your chest.
Did not bother to look up federal law, in my state, that is a crime.
(4)”Impersonate” means to act the part of, assume the identity of, wear the uniform or any part of the uniform of, or display the identification of a particular person or of a member of a class of persons with purpose to make another person believe that the actor is that particular person or is a member of that class of persons.
(B) No person shall impersonate a peace officer, private police officer, federal law enforcement officer, or investigator of the bureau of criminal identification and investigation.