Chris Nassetta, chief executive of Hilton Hotels, who is a Goldman client and longtime friend of Mr. Solomon’s, called him a “genuinely heartfelt, moral, high-quality human being.” Mr. Nassetta added, “Whoever coined the phrase, ‘It’s lonely at the top’ … it really is.”

Another friend, Ted Virtue, said some of the criticism simply came with the job. “The dynamics at Goldman — with all the partners and ex-partners — are that there is just a lot of second-guessing and jealousy,” said Mr. Virtue, chief executive of the private equity firm MidOcean Partners. At the same time, he called Mr. Solomon’s DJing activity an unforced error. “I simply don’t understand it.”

Mr. Solomon, in many ways, remains intransigent about making personal changes that might soften his reputation, according to people who have discussed the matter with him. One example: After a parade of Goldman executives and board members — including many of his allies — over the past year asked him to knock off his high-profile D.J. gigs until the bank reached firmer footing, he ramped down the bookings. In the past 17 months, he has played only two public gigs, according to Mr. Fratto. But Mr. Solomon also insisted to those people that he could restart the gigs at any time.

Last month, at Mr. Solomon’s suggestion, the Goldman board appointed Thomas K. Montag, a former top executive of Bank of America, as a director. The move shocked many people at Goldman because Mr. Montag, who had once worked at the bank, was a polarizing figure whose demanding ways were increasingly out of touch with a changing Wall Street.

Mr. Montag didn’t respond to a request for comment.

Among those whom Mr. Solomon didn’t consult on the hire: Mr. Blankfein, who had passed Mr. Montag over for a promotion before his exit from Goldman two decades earlier.

Emily Flitter contributed to this report.