For non-radio geeks, the United States has not issued three-letter callsigns to broadcast stations in many decades. The stations that have them were issued them in the 1920s. Once the rules changed in 1931, all new calls were 4 letters. If an AM station's owners started an FM or a TV station, they could suffix the AM call appropriately. Otherwise, if you don't have a 3-letter call now, you can't get one. And if you give it up, you can't get it back. Which means that for a post-Cold War station to have the callsign of a hostile intelligence agency, it had to have it before 1930, and had to keep it all through the bad old days.
A page on KGB's history, and another on 3-letter calls tells us this: in 1927, KFBC hired a station manager named George Bowles. Bowles requested a call change, granted in March of '28, to include his own initials--KGB.
The station slogan in those days was "Music for the Sick", which some would probably argue applies just as well to the modern day FM rocker.
Ownership started a simulcast station on the new FM band in 1972. This is the same KGB-FM on 101.5 MHz I wake up to today.
The AM station changed calls in 1982, and again later on, and is now KLSD, carrying the new "XTRA Sports" on 1360 kHz. (The old "XTRA Sports" ran on XETRA 690 AM until dimwit Clear Channel management decided we were "better served" by running it out of Los Angeles. They were forced to divest management of it last year, it's now Spanish talk.) KLSD and KGB-FM are both owned by the Clear Channel World Domination Empire, run out of the same fortress in Kearny Mesa.
As a side note, in my searches, I found an account of the KSON tower blowing over three years ago. If the idea of tons of steel, wired to a 50 kW transmitter, dangling from 300 feet in the air doesn't scare the crap out of you, it should.