Traditional media sometimes suffers from schizophrenia about a Web site’s brand. Should it be named after the newspaper or TV station, or should it have a unique, Web-savvy name?

Some have opted for a pure extension of the traditional product. Two of the biggest examples are WashingtonPost.com and NewYorkTimes.com. Others have chosen a city name such as McClatchy/Knight-Ridder with Charlotte.com.

Quite a few times, media companies have chosen both a brand extension and a unique pure Web brand on top of it, i.e., Landmark’s HamptonRoads.com on top of PilotOnline.com in the Virginia Beach market. Visitors who type in PilotOnline.com will end up in a PilotOnline directory within the HamptonRoads.com umbrella address. Others still have produced a slew of brands — sometimes as many as eight or 10 — in one market.

Let’s take the easy one first. Building a boatload of brands in a single market is fraught with problems. You have to promote multiple sites with multiple campaigns using limited resources.

You lose the ability to move a visitor easily from one site to another. You also run the risk of confusing visitors, especially if each site has a different design and navigation. In quite a few cases, Cox in particular, companies that have tried multiple standalone brands have retreated back to a single one.

These problems are also true but to a much lesser extent for markets with both a brand extension and a unique pure-Web brand, such as the Landmark example. But it makes good business sense for the sake of the core newspaper or TV station to have a strong brand extension.

It also makes sense to look beyond defensive extensions and into the realm of pure plays. A pure play site reaches new audiences and often allows the chance to try new types of content presentation and new types of applications.

It comes down to prioritizing. Media operations are best served by making a strong commitment to their brand extension sites because they bring the most audience and revenue thanks to the strength of the core brand. Start building a pure Web brand, but don’t over-commit, and try to see it as a long-term investment.