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.”