You need a front, usually an international business. Business is useful, because most international businesses function in a remarkably similar fashion to covert operations – they bribe people, seek information, hide funding sources, use postal boxes and rented offices to avoid taxes and get business.
The front needs a “legitimate” contact, someone who can be researched and identified. Someone with minor celebrity, such as being the wife of an ambassador, is just about perfect. Someone like that could be checked by intelligence services and ignored.
These front operations need to actually function like the businesses they claim to be, so they will actually pursue business and fulfill contracts to prove they are real. Some percentage of the employees don’t know they are working for a covert front, and are totally separate from the espionage function.
If the cover on the front is blown, say someone tells the world that the ambassador’s wife is actually an employee for the CIA, there is a problem for everyone associated with the front, not just those who were part of the espionage operation. Counterintelligence people don’t like being fooled, so everyone will be hauled in and considered guilty. There is rarely any effort to allow those people to prove their innocence.
Even if the person at the White House who leaked the information knew all of this, it appears that they didn’t care. All that mattered to them was to exact revenge for making the president look either like he was lying or grossly misinformed in the State of the Union speech. There was no thought about the consequences or collateral damage. But then, someone bent on vengence doesn’t think like that. Much as a nation that goes to war to avenge the murder of an emperor’s nephew — vis World War I — the long-term effects are not seen, and if they are they don’t matter. That’s the scariest part of this story: there seems to be no line they won’t cross to get to their objective.
It makes you wonder what they won’t do.