When they work out well, management consultants bring a fresh perspective to a company that needs one. eBay’s a strange choice for a management consultant’s fresh look, given that its senior-management ranks have been riddled with former consultants since the day Meg Whitman, who started her business career at Bain & Co., walked in the door.All the same, eBay’s new CEO, 47-year-old John Donahoe, not only is talking about challenging conventional wisdoms at the pioneering Web company, he’s actually challenging them. This is one consultant, after all, who can analyze the problem and then implement a plan.

eBay needs one.In an interview Wednesday afternoon after he was named CEO, I asked Donahoe and Meg Whitman what was right with eBay and what needed improvement. Whitman, tellingly and appropriately, deferred to Donahoe. What’s right, he said, is eBay’s “leadership position in e-commerce,” online payments and communications. By the first two he meant eBay.com, the company’s flagship property, and PayPal, the surging leader in Web-based payments. By communications he meant Skype, on which the jury remains out, certainly as part of eBay.

As for challenges, Donahoe said eBay needs to make sure it keeps up. He said eBay.com needs to make itself easier and simpler to use, that its fixed-price sales function needs to be improved and that the company must continue growing PayPal.The last goal isn’t new. PayPal has been an eBay priority for years, and Donahoe noted that PayPal has experienced three quarters of accelerating growth, the type of boast Whitman used to regularly be able to make about eBay overall. As for the first two goals, Donahoe says 2008 will be the time to prove many of the improvements eBay has been readying during 2007. The company has simplified its home page and beefed up its feedback system, particularly with regard to sellers.

Those are incremental changes, though. More critical will be a move Donahoe describes as “challenging the fundamental precepts of eBay.” For example, eBay’s search function long has listed auctions that met user’s criteria but ranked results by the auctions that would end soonest. It was the eBay way, but not necessarily the best way. Beginning this year, the company will roll out a “best match” function, already being tested in Korea and France, that will prioritize the least-costly fixed-price items with the highest seller ratings.

Earlier in the day Donahoe had told investors that eBay’s best days were ahead of it. I asked him how he could justify that optimism, considering the extraordinary past decade. His answer wasn’t quite as incisive as some of his others. “eBay has a timeless, inspiring purpose and mission,” he said. “Our broadest goal is continuing that purpose and mission and in the process build a great and enduring company.” It’s a worthy goal. And a tall order.

Skeptics and other pundits think eBay should boost shareholder value by ditching PayPal and Skype, arguably its greatest and worst acquisitions, respectively. Donahoe shared his thoughts candidly. “We like the businesses we’re in and believe in the synergies,” he said. In particular, he believes in PayPal’s ability to continue to improve the selling experience on eBay. I point out that PayPal might be able to expand its non-eBay business better with the likes of Amazon.com and Google if it weren’t owned by eBay. Donahoe thinks customers will keep demanding PayPal and that its bigger presence creates a “flywheel effect” that will counter competitive threats.It’s debatable if keeping PayPal is the correct decision, but eBay seems serious about it. The elevation of PayPal President Rajiv Dutta, eBay’s longtime CFO, to Donahoe’s former job as president of eBay seems to prove that.Donahoe seems less committed to Skype. He notes that eBay only installed its own management team at Skype two months ago and asserts that “we’re just getting around to the position where we can test the synergies.” Mark a Skype sale as to be determined.

Finally, I asked Whitman what her plans are for after March 31, when she steps down as CEO. She’ll remain on the board of eBay, where she plans to focus her energies in 2008. She’s also a director of Procter & Gamble (PG) and Dreamworks (DWA). She’s working on her family’s new foundation and also as a national finance chairman for Mitt Romney, a personal friend from her Bain days. Asked what she’ll do in 2009, she responds, “I don’t know about that.”

A tradition at eBay is that the people who work with its senior executives get to name their personal conference rooms. The meeting place belonging to John Donahoe, the top executive for eBay’s core online marketplace, is Dennis the Menace. If the Wall Street Journal’s sources are right and Donahoe is named the next CEO of eBay when Meg Whitman retires, he’ll likely start causing mischief almost as soon as he’s in the top job.

Donahoe isn’t nearly as well known as Whitman, the public face of eBay (EBAY) for a decade. But he’s no newbie. He’s been at the company for nearly three years now — a tough three years given that he presides over eBay’s thorniest problem, its slow-growth online sales engine. eBay’s missed opportunity is gargantuan. Compared with Amazon.com’s (AMZN) business, for example, eBay.com enjoys a well earned monopoly and the rich profit margins that come from holding no inventory. Yet, as I’ve commented recently,  competitors like Amazon and Google (GOOG) have out innovated eBay, decimating its stock. (Meg Whitman claims to not follow eBay’s stock price. Read my account of the company mid-malaise, about a year ago.)

There already are signs Donahoe has taken the reins at eBay. In early December he spoke at a UBS conference and hinted strongly that major changes were afoot in eBay’s fixed-price sales business. eBay’s sellers have felt nicked and dimed by the company for years. Donahoe suggested that eBay will tinker with its pricing model by lowering upfront prices and raising closing commision fees. The lowering part spooked Wall Street, even if it’s the right thing to do. (It’s a lot like economic stimulus: Lower taxes in hope of expanding the economy. eBay’s not the U.S. government though … if it lowers upfront fees and doesn’t convert the sale its revenues go down.) An insidery writeup of Donahoe’s talk appeared here.

The other big decision facing Donahoe is what to do with PayPal, the eBay-owned payment business that is roaring. Late last year PayPal quietly juiced up its management team, making four key hires of prominent executives who worked at blue-chip companies including Avon (AVP), American Express (AXP), McKinsey, Oracle (ORCL) and Visa. PayPal’s growth engine is its business selling services to online merchants other than eBay, making eBay’s ownership of PayPal less necessary. It’s hard to imagine that PayPal was able to attract such top talent by offering stock packages merely in eBay stock options. Asked if the news was evidence that eBay was planning to spin off or sell PayPal, a PayPal spokeswoman responded: “This shows the caliber of people that want to leave fantastic jobs at fantastic companies to come to PayPal. There are no plans to change PayPal’s structure within eBay.”

The question remains what John Donahoe will do at eBay, assuming he gets the job. (I used to think Jeff Jordan had a lock on the job; I was wrong.) Donahoe is quite literally the Mitt Romney of the Internet world. He’s a Bain consultant through and through, a handsome guy with a gigantic Rolodex (note to kids: that’s where people Donahoe’s age, 47, used to keep their contacts; it’s now a metaphor) and a bias toward action.

Be certain of one thing, should the man insiders call Dennis the Menace get the job, expect some mayhem in the near term.