The Fortune 500 comes out just once a year, but the companies on it make headlines every day. Here then are today’s highlights of news and happenings coming from the biggest names in business.

By Shelley DuBois, reporter

FROM THE GALLEON TRIAL Goldman Sachs CEO Lloyd Blankfein said he had “an inkling” that during Rajat Gupta’s time as director of Goldman (GS), Gupta passed classified information onto hedge fund founder Raj Rajaratnam. The trial is the biggest insider trading case of this generation. So far, Goldman has been accused of no wrongdoing linked to the Galleon trial. [Wall Street Journal]

SECOND FIDDLE An investment banker from Morgan Stanley (MS),Owen O’Keeffe was also called to the stand to answer questions from prosecutors trying to figure out if a Morgan Stanley employee leaked insider information to Rajaratnam. But Goldman seemed to loom much larger–one of Rajaratnam’s defense lawyers referenced the wrong bank while questioning O’Keeffe. “Sorry,” the lawyer said, “I have Goldman Sachs on the mind.” [New York Times]

BEHIND OTHER BANKS While other banks are shaking off their crisis-era restrictions, the Federal Reserve refused to clear Bank of America (BAC) to raise its dividends. Bank of America, along with Capital One, failed the Fed’s latest round of “stress tests.” Stock prices increased for the other banks that passed. [Wall Street Journal]

CONOCO’S LIQUIFICATION SPREE continues as the company plans to shed between $5 billion and $10 billion in assets over the next two years. This is a continuation of Conoco’s (COP) asset sales strategy outlined in 2010, in which the company says it will shrink so it can boost its production per share. [Wall Street Journal]

BP ALSO SHEDDING ASSETS, STILL, the latest being a natural gas processing plant in Colorado, which BP (BP) is selling to Anadarko Petroleum for $575.5 million. The deal represents one more step towards BP’s goal of raising $30 billion to pay off financial obligations from last year’s oil spill in the Gulf of Mexico. [Financial Times]

FUNDAMENTAL FLAW REVEALED in BP’s blowout preventer in a report filed by investigators. The engineers commissioned to issue the report say that the blowout preventer didn’t close properly because of a design flaw, not because BP operated it incorrectly.  Other investigations have suggested that a series of poor decisions on BP’s part did cause the initial blowout. [Wall Street Journal]