President-elect Donald Trump named Republican National Committee Chairman Reince Priebus as his chief of staff, a selection that suggests the Republican is interested in a more conventional approach to governing after his insurgent campaign.

Mr. Trump on Sunday also named Stephen Bannon as his chief strategist and senior counsel. Mr. Bannon, who was chief executive of the Trump campaign, was in consideration with Mr. Priebus for the White House’s top personnel position.

“Steve...