WASHINGTON—President Donald Trump has elevated Chris Liddell, who now serves in a White House office aimed at streamlining the federal government, to deputy chief of staff for policy coordination, the White House press secretary said Monday.

Mr. Liddell, a former Microsoft Corp. and General Motors Co. executive who was under consideration earlier this month to serve as the next director of the National Economic Council, will be a second deputy to White House Chief of Staff John Kelly. Mr. Trump last week named CNBC commentator...