For the rank and file, there is a safe distance between their company’s reputation and their own. But that is not true at the top: Chief executives’ identities are inextricably linked to the corporations they run and vice versa. That symbiotic relationship, however, has its problems. Must C.E.O.’s and their companies be seen as one and the same? And if so, does failure as C.E.O. mean that an executive’s next career level after the top spot will be, well, the bottom?

To get perspective, I broached the issue with Shelly Lazarus, who since 1996 has been chief of Ogilvy & Mather Worldwide, a $2 billion global marketing firm that has dispensed brand-building advice to American Express, Dove, I.B.M., and oil giant BP (whose leader, John Browne, resigned in May following revelations that he lied in court about his love life).

Lazarus’ position on the matter of C.E.O. image is unequivocal: In today’s online, 24-7 news world, separating the chief’s personal identity from the company’s is simply not an option. “Everything a C.E.O. says and does is no longer personal,” she says. “It is attributed to the company.” Case in point: Former HBO chief Chris Albrecht, who in May was arrested for allegedly assaulting a female companion in Las Vegas, lost his job before his illicit behavior could tarnish the network’s image.

Not only do personal issues become the company’s problem, but a company’s poor performance will be attributed to the person in charge, even if he or she was not directly responsible for whatever debacle is making headlines. “I can’t think of many cases in which the company failed but the chief came out on top,” says Lazarus. Consider JetBlue’s failure to communicate with passengers and permit them to deplane during a February snowstorm. By May, founding chief David Neeleman was forced to resign despite apologizing to customers on TV, in print, and via email.

It’s likely that both Neeleman and Albrecht lost their jobs because, as leaders, they were regarded as indistinguishable from their companies. “Ultimately,” says Lazarus, “the leader bears the responsibility for everything that happens”—good or bad.

There’s something ironic in all of this. Since the mid-1990s, ambitious professionals have been told to establish their own personal brand rather than have their reputation hinge on any one organization. In 1997, management consultant Tom Peters encouraged us in a Fast Company cover story to become “C.E.O.’s of our own companies: Me, Inc.… Head marketer for the brand called You.” But an executive’s efforts to develop an individual brand must be scrapped once he or she takes the helm of a company. Cautions Lazarus, “The company’s brand must take precedence over your own personal brand.”

If a public relations disaster comes, an organization has a chance for redemption if the chief quits. But what becomes of the quitters? Who will hire, for example, David Neeleman?

Lazarus believes the American public can be very forgiving of leaders as long as they say they are sorry with humility and grace. As Neeleman knows, boards and shareholders are far less indulgent. Making things worse, says Lazarus, is that “corporate lawyers tell chiefs not to apologize” because it can come across as an admission of guilt, which can have costly legal ramifications for the organization. Lazarus believes Neeleman was right to issue a public apology. Despite his current unemployed status, his mea culpa probably helped restore his professional reputation. I even feel a little sorry for him. Granted, I wasn’t stuck on a grounded JetBlue plane for hours.

When I ask Lazarus how she manages her own public image, she says, “I don’t manage it.” But she is selective about her public appearances. She receives hundreds of speaking requests and invitations to events every year but turns down the majority of them. “One venue might mean greater glory for me personally,” she says, “but if I can’t figure out how it would be of any help to Ogilvy, I don’t go.” It’s not that she doesn’t appreciate the accolades or attention from her colleagues; it’s just that she’d rather spend her time with current or potential clients.

Lazarus also admits that it is tiring to be out front all the time. She tries to escape her company persona by vacationing at her small house in Sheffield, Massachusetts. “There, I am just the lady who lives in the house on the corner,” she says. But come Monday morning? “C.E.O.’s are in the public eye; that’s just the way it is,” she says. “My own success or failure will be the same as the success or failure of the company.”