Republican Rep. Jim Bridenstine, named on Friday as President Donald Trump’s choice to head the National Aeronautics and Space Administration, faces tough policy, personnel and political challenges repositioning the agency in an era of booming commercial space ventures.

The decision to nominate the former Navy aviator and three-term Oklahoma lawmaker, a move that had been expected, comes amid lingering uncertainties surrounding the White House’s broad space goals. A space policy council, headed by Vice President Mike Pence,...