Gov. Katie Hobbs of Arizona, a vulnerable Democrat running for re-election, plans to tap a longtime Republican and former mayor of a Phoenix suburb to serve as her running mate, according to two people familiar with the decision. John Giles, a former mayor of Mesa, Ariz., is expected to be announced in the coming days as Ms. Hobbs’s lieutenant governor nominee. Neither Ms. Hobbs nor her campaign would confirm the choice, and nothing is final until an announcement. But the apparent pick is a nod to bipartisanship in a campaign that will pit Ms. Hobbs, a low-key Democrat, against Representative...