Wyman is the head of House Manderly, a prominent Northern house.
Lord Wyman Manderly fought in the War of the Five Kings for Robb Stark, however, after his son and heir Wendel Manderly was slain during the Red Wedding, he decided to take no part in the Bolton and Stark conflict and stayed at White Harbour to ensure no more Manderly lives would be at risk.
House Manderly plays no role in the Battle of the Bastards, having refused summons from both House Stark and House Bolton to keep his house and vassals from suffering more deaths after the War of the Five Kings. After Jon takes Winterfell, Wyman and the other Northern lords arrive to treat with him, and get berated by Lady Lyanna Mormont for not upholding their oaths of allegiance to House Stark despite the crimes committed against them and their families at the Red Wedding. Wyman is consequently the second lord to declare Jon Snow the new King in the North and the first to call him the "White Wolf".
Head of one of the North's main houses, Wyman Manderly refused to commit his men to the Starks after his son died at the Red Wedding. Since won over by Jon's leadership at the Battle of the Bastards, Lord Manderly was the first to declare him King in the North.