(Corrects 3rd paragraph to show Castro-Wright was put in charge of global sourcing in 2008)

CHICAGO - Wal-Mart Stores Inc on Tuesday named Bill Simon to run its U.S. discount stores, which have struggled with sluggish sales as their core customer continues to be pressured by high unemployment.

The move allows Eduardo Castro-Wright, who had headed the U.S. unit, to move to California and be with his wife, who is recovering from a heart transplant, Castro-Wright said in a memo to employees.

Castro-Wright, 55, will continue as vice chairman of the world's largest retailer and as head of the company's global e-commerce initiatives and global sourcing, assignments he has had since January and 2008, respectively.

Simon, 50, had been chief operating officer of Walmart U.S. He takes over a business that has seen sales at stores open at least a year fall in each of the last four quarters.

That business has been hurt both by the economy and by Wal-Mart's own missteps, including a move to pare the number of items carried in Walmart stores. That cost the company sales as shoppers who could not find their favorite items, even if they were not big sellers, did all their shopping elsewhere, Wal-Mart has said. The company has been restoring some items and has announced price cuts on thousands of items in a bid to boost U.S. traffic.

Chief Executive Officer Mike Duke stressed the need for the company to improve its e-commerce businesses and the company has also said the international business would be a key growth engine.

Analysts do not expect much change at the company's more than 3,700 U.S. discount stores, at least early on, as Simon on Tuesday stressed the need to build traffic and make sure the stores had the right product assortment, initiatives that were already under way.

It's still all about them managing expenses and trying to leverage expenses and that's all about getting the topline (sales) going again, Edward Jones analyst Matt Arnold said.

Walmart has a strong lineup of top managers that help make transitions like the one announced on Tuesday easier, which is shown when the company's top managers are paraded before analysts at big meetings, he said.

It's pretty easy to see that they have impressive bench strength, Arnold said. It's not like they have one or two people.

Simon came to Walmart from restaurant chain operator Brinker International Inc , where he was senior vice president for global business development. He also served as secretary of the Florida Department of Management Services, appointed by then-Governor Jeb Bush.

Walmart shares were down 1.7 percent at $48.73 in morning trading on the New York Stock Exchange.

(Reporting by Brad Dorfman, editing by Gerald E. McCormick, Dave Zimmerman)