A consulting firm hired by Burisma Group mentioned that former U.S. Vice President Joe Biden’s son served on the Ukrainian gas company’s board so the firm could leverage a meeting with the State Department, according to documents and a former U.S. official.

The documents—email exchanges between State Department staff members made public this week—show that the consulting firm, Washington-based Blue Star Strategies, used Hunter Biden’s name in a request for a State Department meeting and then mentioned him again during the meeting as part of an effort to improve Burisma’s image in Washington.

Mr. Biden was appointed to the Burisma board in 2014, when the company and its owner faced allegations of corruption, and he remained there until April of this year.

It isn’t clear whether the younger Mr. Biden knew his name was being used by Blue Star in its contacts with State Department officials on Burisma’s behalf in early 2016. A lawyer for Mr. Biden didn’t respond to a request for comment.