After five unprofitable years, Liz Claiborne Inc. sold off its namesake brand to repay its debts and is now looking to attract a richer consumer with a trio of higher-end brands. The only thing it’s missing? A new name.

The company, which owns Juicy Couture, Kate Spade, and Lucky Brand, agreed Wednesday to sell its namesake department-store label to J.C. Penney for $267.5 million. It also previously jettisoned some other brands, including Monet, also sold to Penney's, its Mexx division, which is being sold to the Gores Group, the Dana Buchman label, which is being acquired by Kohl’s.

These, and some other similar shifts, have helped the company raise $471 million, virtually all of which will be used to pay down debt, notes Women's Wear Daily. Wall Street seemed to approve, and Liz Claiborne stock was up 34.1 percent after the announcement, to $6.84, and was trading above $7 this morning.

But now that the company’s fortunes seem to be turning around, what can it do about its name? And how should an existing company or a startup go about developing a name, anyway? We came up with five questions for brand naming and strategy specialist Scott Milano, owner and managing director of Tanj Branding LLC, a New York City-based consultancy. Milano came up with the names “Ally Bank,” the Nintendo “Wii” and Sony “Bravia” television.

Portfolio.com: Should Liz Claiborne Inc. choose one of its labels—Juicy Couture, Kate Spade, and Lucky Brand—and make it the umbrella name of the new company ( à la Gap, Inc.)? If it does choose one of the existing labels it already owns, should it go with the best-known brand? The most profitable one?

Milano: While focusing your attention on premium-label brands makes business sense, pinning your corporate brand to an existing label name does not make brand sense. If the leadership team has learned its lesson, it has realized the need for an entirely new umbrella name for the company. Having the verbal DNA of the Liz Claiborne name throughout all aspects of your portfolio—at the corporate and product levels—may have worked well during good times, but as soon as the company needed to sell any brands that have “Liz Claiborne” in them, their portfolio of names crumbled.

Choosing a product brand name like Juicy Couture or Kate Spade to cover the entire portfolio is like trying to make a sock into a full bodysuit: There’s just not enough stretch. Each of these brand names represents a specific market. While they have “name recognition” and the company already owns the trademarks, they are not suitable for housing the entire portfolio. Elevating one above the rest could cause damage and confusion with investors and consumers. And what happens if one day the company decides to sell the label that it has also chosen as the corporate name? It’s back to square one.

In this case, there’s no compelling reason to use the name of the company’s best-known or most profitable label brand also as its corporate name. The risks are just too high. You might be able to make a case for using one of the company’s existing names if its pulled from a stock of unused or hardly used names, or if the company went down the route of resurrecting a long-lost heritage name from its past. But without evaluating individual names, that’s a lukewarm approach at best.

So what is the benefit of a new name?

An entirely new umbrella name for the company will offer a fresh start. It will allow the company to focus its resources on its higher-end, more successful labels that will drive the business forward. It will provide the stretch and flexibility the new streamlined portfolio demands.