LONDON—As the fashion elite filed into St. Paul's Cathedral on Monday to memorialize British designer Lee Alexander McQueen, the company he left behind is on the brink of making its first crucial trip down the women's catwalk without him.

The late Mr. McQueen, who built his label into one of the world's most daring fashion names, committed suicide last February. Four months ago longtime deputy Sarah Burton took over as creative chief of the London-based Alexander McQueen label, a small but symbolic part of PPR SA's Gucci Group.

Now, as Ms. Burton gears up to unveil her first full women's wear collection in Paris on Oct. 5, the label faces a tough question: What does it mean to be Alexander McQueen without Alexander McQueen?

The strategic challenge highlights a longstanding problem in the fashion industry, where it's difficult to replace high-profile designers who become indivisible from their eponymous brands.

Mr. McQueen's shows were highly produced feats of shock and awe. In an address during the service on Monday, fashion columnist Suzy Menkes called his trademark 2009 armadillo shoes "some of the most chillingly misogynist footwear we have ever seen on the runway." His 1995 collection, "Highland Rape," which featured strutting nudity and ripped Tartan dresses, symbolized what he called the rape of Scotland by the British.

"I had no doubt, and nor did he, that he was an artist who just happened to work with clothing," said Ms. Menkes. "Above all, we all understood that Lee's work was deeply personal."

Gucci Group must now make the label stand on its own, apart from the personality that made it. Whether that means continuing the tradition of such scandalous designs is unclear.

"The creation of modern beautifully crafted clothes was at the heart of Lee's vision. I intend to stay true to his legacy," Ms. Burton said in a statement released by Gucci Group in May, her only public comment on the matter.

Having worked under Mr. McQueen for 14 years, most recently as head of design for women's wear, she is well-placed to understand his vision. Like Mr. McQueen, she was born in Britain and trained at London's Central Saint Martins College of Art and Design. She joined his label before she graduated. But as a chief designer, she remains an unknown quantity. Gucci Group declined to make Ms. Burton available for an interview.

Gucci Group, which acquired a majority stake in Alexander McQueen in 2000, has said it is committed to keeping the McQueen business alive, but the fledgling label has lost money for years, breaking even for the first time in 2007. Ms. Burton has to carve out an artistic vision that is her own, but she also must design clothes that can help lift the business out of its start-up phase.

That could be a strong point for the new chief designer: Much of her job at Alexander McQueen entailed boiling down the designer's catwalk creations into products that would be sellable on store shelves.

One possible avenue for the company is to focus on growing its secondary label, McQ, and developing new and existing licensing contracts for things like perfume and sunglasses.

When it comes to his appeal on the runway, "I don't think anyone will be able to keep up with McQueen," said fashion consultant Robert Burke, president and CEO of Robert Burke Associates. "I think it would probably be best to not try to compete with that." But he added: "Keeping consistency with the brand is really important. Any kind of major departure would not be good."

Though the McQueen label has received recognition and publicity in the wake of Mr. McQueen's death, Antoine Belge, a luxury-goods analyst at HSBC, said the company should be wary of trying to grow the brand into a huge phenomenon.

"Gucci Group should try to make it a bit more sizable whilst maintaining its 'niche' positioning," Mr. Belge said. "This is never easy for a brand to do this, since it will require it to launch products accessible to a broader audience without alienating the core clientele."

Some labels have successfully replaced icons. One example is Calvin Klein: After the designer sold his fashion empire to private-equity firm Phillips-Van Heusen PVH -1.18%in 2003, his longtime protégé Francisco Costa took over creative duties and has received significant acclaim.

But it has often been more difficult. Gianni Versace SpA, for instance, suffered for years after its founder was murdered in Miami, until Donatella Versace managed to replace her brother as a guiding artistic force behind the label.