The specialty health insurer formerly known as UICI has taken the name of its best-known subsidiary, HealthMarkets Inc.

Managers, company agents and others recently used private equity from The Blackstone Group L.P., New York, and other firms to take HealthMarkets private.

Managers now are trying to use some of the private equity to relaunch HealthMarkets, North Richland Hills, Texas, as a major player in the personal health account plan market.

HealthMarkets divisions that are part of the original UICI business sell limited-benefit health plans, student health insurance plans and plans for self-employed individuals.

UICI acquired the business that became its HealthMarkets division, HealthMarket Inc., in September 2004.

Stephen Wiggins, the entrepreneur who founded Oxford Health Plans Networks Inc., Trumbull, Conn., founded HealthMarket Inc. in Connecticut in 1999. Wiggins’ company has been a pioneer in efforts to give program members provider-by-provider, procedure-by-procedure price information.

Today, the business Wiggins built sells personal account health coverage programs in 44 states. In 19 states, the company offers Web-based systems that give patients price information for more than 20,000 health care procedures, HealthMarkets says.

The new HealthMarkets will be running print ads in publications such as USA Today, The New York Times, People and Money Inc. and on a variety of Web sites, such as Google and Yahoo!, to emphasize that it has the information that could help solve a crucial problem in the U.S. health finance system.

“One big reason health care costs go up every year far faster than inflation is that the people who pay the bills have no idea how much things cost,” HealthMarkets President William Gedwed says in a statement.

HealthMarkets can cure that lack of transparency by showing plan members how much medical procedures actually cost, the company says.