One Wall Street quipster said they should have renamed the brokerage firm "Bache Ball" because its new chief executive, George L. Ball, gets so much attention.

Instead, the more mundane name Prudential-Bache Securities Inc. was chosen. But there is no mistaking the fact that Ball, who left the presidency of the E. F. Hutton Group Inc. to join the firm in July, has every intention of leaving his mark on the staid, sometimes controversial Wall Street brokerage house.

The recent announcement that Bache Stuart Halsey Shields Inc. would become Prudential-Bache has focused more attention on Bache and Ball, but it is only the beginning of a major program to integrate the giant insurance firm with the brokerage house it bought for almost $400 million 19 months ago.

It was not even the first time in recent days that attention had focused on Bache. Just a week before the name change was announced, Ball irked his former associates by swiping three key members of Hutton's leadership team: research director Gregory Smith, investment strategy chief Fred Fraenkel and Hutton's widely known chief economist, Edward Yardeni.

Snagging the three was no small coup. They were among four Hutton executives pictured in a full-page advertisement in the October issue of the influential financial magazine "Institutional Investor." The ad quoted, in large lettering, a May article in the same magazine as saying, "dramatic changes have come to E.F. Hutton's research department." Sadly for Hutton, the changes since that ad was published are even more dramatic.

Nor did the personnel shifts bring Bache its first headlines last month. The New York Stock Exchange fined Bache a record $400,000 for its involvement as a broker in a massive silver speculation scheme by the billionaire Hunt brothers. Ball was not at Bache during the 1979 to 1980 period in question and said the fine was paid to help bring the silver saga to a close.

It is Ball's view that, as a result, he will now be able to focus the attention of the firm and its 9,000 employes on meshing the nation's largest life insurance company, which has more than $62 billion in assets, with the sixth largest brokerage firm, which has capital of more than $400 million.

Although he is not viewed as a stock technician, in 20 years at Hutton Ball gained wide respect here for his general management skills, his public work on behalf of securities industries issues, and for getting production from Hutton's sales team.

His brokerage admirers say those skills make him well equipped to turn around Bache, notorious for mounting balance sheet losses and low brokerage productivity. Hutton led Wall Street in brokerage productivity during Ball's tenure.

A corporate reorganization, which moves all Prudential-Bache business into eight discrete yet unified segments, was simultaneously announced with the name change.

According to Ball, "the retail line was going one way, the marketing group another." The changes "provide unblurred lines of authority and shift a number of functions to the most logical organization nexus," he said.

The recent hiring of the former Hutton executives is part of Ball's plan to create "world class research" at Bache and integrate it firmly into the money management end of the company.

In addition, Bache has virtually no reputation in the investment banking business, and Ball wants to change that. He hopes to put Bache into a position to become expert in shelf registration planning and other innovative financing areas and to take advantage of Prudential's formation last January of Prucapital, utilizing Prudential's regional corporate finance department in lending and leasing.

But there has been little evidence up to now that Prudential and Bache know much about working together. And observers say there has been a certain "guardedness" between the two concerns.

But Ball, 43, who is technically the new firm's president and chief executive officer, and his crew believe that there is more synergy -- a merger cliche -- between Prudential and Bache than between other major financial services and their partners which merged and captured the industry's attention two years ago.

But the case for the brokerage-house takeovers has yet to be made with any degree of certainty. It has yet to be proven that the amalgamation of the American Express Co. and Shearson Loeb Rhoades Inc. is a perfect match, or that Sears, Roebuck & Co. knows exactly how it's going to benefit from ownership of Dean Witter Reynolds.

In Ball's view, however, Prudential's money management background, its ability to manage a huge operation and its enormous existing customer base make it the perfect match for an institution such as Prudential-Bache, which sells other financial services. That's why he shocked E.F. Hutton three months ago and jumped to Bache.

That's also why a nationwide advertising campaign is urging the public to "Bring Us Your Future." The effort, which premiered on each of the three major commercial networks on Election Day, will cost Bache about $3 million this month alone. That's equal to the firm's entire advertising expense for the first 10 months of this year. "We think the name is very powerful and something more than just theatrical," Ball said.

Ultimately, Ball said, the company's brokers will be selling Prudential insurance and the lines will blur between the customer operations of the two organizations. But the advertising theme indicates that the company also wants to make a major mark in the broad consumer financial market. "We want to be in the forefront of the ranks of financial planning advisers," Ball said.

Of course, none of this talk of synergy means Ball plans to ignore the basic brokerage business. He has just instituted an expansion of Bache's training program and has brought in 650 newcomers to learn to be stockbrokers.