For Trump, Doug Burgum Emerges as a Safe Option, and a Wild Card

After taking his software company public in 1997, Doug Burgum gathered a few colleagues in his office and swore them to secrecy.

He wanted to uphold the modesty and decorum central to his North Dakota birthright and his chimney-sweeper past, but he was eager to boast about a splashy new purchase. While others splurged on cars or boats, Mr. Burgum’s big reveal was a Bobcat front-end loader — a dirt mover for his ranch near Fargo.

“I remember thinking, ‘Yeah, Doug, you’re not big-timing anyone with that one,’” Jeff Young, the software company’s former operations chief, recalled with a laugh.

Now the governor of North Dakota, Mr. Burgum’s long-held scruples over being seen as an attention-monger have hurled the longtime Republican out of political obscurity and into the limelight as one of a handful of the leading contenders in Donald J. Trump’s search for a running mate.

Mr. Trump’s campaign has requested personal information and other documents from a broad field of potential vice-presidential candidates, including Mr. Burgum, both as part of its vetting process and as a media strategy to build suspense ahead of a formal announcement planned for next month at the Republican National Convention, according to three people briefed on the process who insisted on anonymity to discuss private conversations.

But Mr. Trump appears to have narrowed his focus to contenders with the ability to run a disciplined campaign, the people said. Reducing the potential for unwanted distractions has become increasingly important for a presidential candidate convicted last month on 34 felony charges and still facing multiple other legal problems.