Come up associated with

CIA penetration by the KGB and what amounted to their joint spying on the military was a fact we accepted during the 1950s and 1960s, even though most of us in the Pentagon played spy versus spy as much as we could; those of us, like me, who’d gone to intelligence school during the war and knew some of the counterespionage tricks that kept the people watching you guessing. We would change our routes to work, always used false information stories as bait to test phones we weren’t sure about, swept our offices for listening devices, always used a code when talking with one another about sensitive subjects. We had a counterintelligence agent in the military attaché’s office over at the Russian consulate in Washington whose friends in the Soviet army trusted the KGB less than I did. If my name came up associated with a story, he’d let me know it. But he’d never tell the CIA.

The Day After Roswell

Hi. What does the "come up associated with" mean here? And grammatically, why can "come up" take "associated with"?

Thank you.