Another plea for the ouster of WellPoint Inc. CEO Angela Braly is spurring discussions among investors and analysts about who might be tapped to replace her.

Royal Capital Management LLC, with 837,800 shares of WellPoint as of June 30, urged the health insurer’s board to remove Braly in a letter that was made public Thursday. In doing so, the New York-based hedge fund became the third stockholder in a month to publicly question management at the second-biggest U.S. health care insurer.

While the WellPoint board has supported Braly in two public statements, Jason Gurda, a Leerink Swann & Co. analyst in New York, said investors have suggested James G. Carlson, the chief of Amerigroup Corp., and David B. Snow Jr., the former chief of Medco Health Solutions Inc., as CEO candidates.

Indianapolis-based WellPoint is buying Amerigroup, a rival insurer, for $4.9 billion. Medco was recently acquired for $29.1 billion in April by Express Scripts Holding Co., a fellow drug-benefits manager.

“Certainly, they’re both successful and they’re both available,” Gurda said. “Some investors are looking for a change.”

While neither man has publicly expressed interest in the job, and WellPoint’s board has expressed confidence in Braly, that hasn’t stopped the speculation, he said.

Other names raised by investors include Gail Boudreaux, the head of the health plan division at UnitedHealth Group Inc., the biggest U.S. medical insurer, and Kenneth Goulet, WellPoint’s executive vice-president, said Thomas Carroll, a Stifel Nicolaus & Co. analyst in Baltimore.

Efforts to reach Snow through former Medco colleagues Thursday were unsuccessful. Maureen McDonnell, an Amerigroup spokeswoman, and Daryl Richard, a UnitedHealth spokesman, declined to comment on the CEO speculation.

Kristin Binns, a WellPoint spokeswoman, said executives are meeting with shareholders “to understand their views and share what we are doing to move the company ahead strategically and improve our execution.”

“These are challenging times for many companies in the managed care field, but we believe we are well positioned to win in the market,” Binns said in an e-mail. “We recently announced two acquisitions that position us well for growth in the future, and we are putting in place the team to execute on our opportunities.”

In its letter to the board, dated Aug. 22, Royal Capital wrote that Braly has “failed miserably” since becoming CEO in June 2007. The statement, signed by partners Robert Medway and John Lancefield, cited disappointing profits, a stock that’s lagged behind competitors and “managerial blunders.”

“It is incumbent upon the board of directors to fulfill its fiduciary responsibility to shareholders by changing leadership,” the hedge fund said in the letter.

Braly, 51, has come under fire since the company cut its full-year forecast last month after earnings missed analyst estimates for the second time in three quarters. WellPoint’s market value through yesterday had declined about $8.8 billion since Braly became chairman of the board in March 2010, and the quarterly results prompted two shareholders, investment fund Orbimed Advisors LLC and hedge fund Omega Advisors Inc., to go public with criticism of management.

WellPoint shares were down less than 1 percent Friday morning, to $57.35 a share. They had dropped 2.9 percent in the past 12 months through Thursday. UnitedHealth, based in Minnetonka, Minn., has gained 20 percent in the same 12-month period and increased 58 percent since Braly took on WellPoint’s chairmanship.

WellPoint announced its deal in July for Amerigroup, seeking to become the top provider of Medicaid coverage for the poor as President Barack Obama’s health-care law expands the federal-state program. That may mean Braly is probably safe at least until the end of the year, when the acquisition is expected to close, said Erik Gordon, a University of Michigan business professor who follows the health industry.

While the board has backed Braly, “in the investor world, people have talked about potential replacements,” Brian Wright, an analyst with Monness Crespi Hardt & Co. in New York, said.

The conversation usually starts with Snow and Carlson, CEOs respected for their insurance backgrounds as well as the lucrative deals they crafted for shareholders, he said.

Snow was Medco’s first and only CEO, joining the Franklin Lakes, N.J.-based company shortly before it was spun off from drugmaker Merck & Co. in August 2003. He built the company into the country’s biggest manager of pharmacy benefits by drug spending, serving employers, unions and big insurers like UnitedHealth.

By the time Snow left, Medco’s sales had more than doubled, to $70 billion last year, and its share price had risen almost sixfold. Last year, the company announced its sale to Express Scripts, its St. Louis-based rival, for a 28-percent premium on its shares.

“People think he did right by his shareholders,” Wright said.

Before Medco, Snow was president and chief operating officer at Empire Blue Cross Blue Shield, a New York State health plan later bought by WellPoint. He also held executive positions at insurers including Oxford Health Plans, now owned by UnitedHealth, according to a Medco biography.

Carlson, 60, has been CEO of Amerigroup since September 2007, and an executive since 2003 at the Virginia Beach, Va.-based plan. WellPoint agreed to buy the company at a 43-percent premium.

Through the deal announcement, the insurer’s share price doubled and enrollment rose 76 percent. Carlson previously was president at UnitedHealth from 1995 to 1998, said Carl McDonald, a Citigroup analyst, in a July 16 note to clients.

“He was quite successful at his last company; he used to run a big commercial operation, and he has a significant amount of cachet with investors,” McDonald wrote. “Before, WellPoint’s board didn’t have a lot of obvious choices if they wanted to go in a new direction with the leadership of WellPoint, but that’s no longer the case.”

Still, McDonald said, the fact that Braly would bring a potential challenger like Carlson into the company, suggests her standing may be “a lot more secure than those of us outside the company perceive.”