Chelsea Clinton was alarmed.

During a 2011 trip to London representing her family’s foundation, she got wind that people close to her father, Bill Clinton, had been lobbying members of Parliament for their own consulting clients, telling the officials they were calling “on behalf of President Clinton.”

People she ran into whispered that the practice reminded them of former Prime Minister Tony Blair’s sneered-upon post-Downing Street moneymaking ventures, a comparison that she said “would horrify my father,” who had no idea his name was being used.

It was an eye-opening moment for Ms. Clinton, the only child of America’s most famous political power couple, who was making a new name for herself as a defender of her father’s legacy and, by extension, of her mother’s coming second presidential campaign.

Her comments about her father’s aides were revealed in the thousands of emails obtained by hackers and released by WikiLeaks over the past month. In addition to showing the internal strategizing, sniping and off-the-cuff commentary within Hillary Clinton’s inner circle, the emails paint an unexpectedly detailed portrait of Mrs. Clinton’s guarded and private daughter as she set about her goal, as she explained in one email, of “protecting my father and the nonprofit status of the foundation.”