...and we have at least two examples.
Ramsay is the bastard son of Roose Bolton. In season 4 Roose had a decree from the crown made up to legitimise Ramsay.
Roose: The North is larger than the other six kingdoms combined. And I am the Warden of the North. The North is mine. Now tell me, what is your name?
Ramsay: Ramsay Snow.
Roose: No, not Ramsay Snow. Open it. From this day until your last day, you are Ramsay Bolton, son of Roose Bolton, Warden of the North.
Game of Thrones, Season 4 Episode 8, "The Mountain and the Viper"
Upon hearing Walda Bolton, Roose's wife, has given birth to a baby boy Ramsay stabs his father and kills him. At this moment Ramsay becomes Lord Bolton.
Ramsay: Maester Wolkan, send ravens to all the Northern houses. Roose Bolton is dead. Poisoned by our enemies. How did he die?
Maester Wolkan: Poisoned by his enemies.
Lord Karstark: You're talking to your lord. Use respect.
Maester Wolkan: Forgive me, my lord.
Game of Thrones, Season 6 Episode 2, "Home"
Jon is the bastard son of Ned Stark.
He's not but he is widely believed to be.
After leaving the Nights Watch on grounds of having died he takes over Winterfell and the North in the Battle of the Bastards against Ramsay Bolton. After the battle he becomes the King in the North.
Lyanna: Your son was butchered at the Red Wedding, Lord Manderly. But you refused the call. You swore allegiance to House Stark, Lord Glover, but in their hour of greatest need, you refused the call. And you, Lord Cerwyn, your father was skinned alive by Ramsay Bolton. Still you refuse the call. But House Mormont remembers. The North remembers. We know no king but the King in the North whose name is Stark. I don’t care if he’s a bastard. Ned Stark’s blood runs through his veins. He’s my king from this day until his last day.
Manderly: Lady Mormont speaks harshly and truly. My son died for Robb Stark, the Young Wolf. I didn’t think we’d find another king in my lifetime. I didn’t commit my men to your cause ‘cause I didn’t want more Manderlys dying for nothing. But I was wrong. Jon Snow avenged the Red Wedding. He is the White Wolf. The King in the North.
Glover: I did not fight beside you on the field and I will regret that until my dying day. A man can only admit when he was wrong and ask forgiveness.
Jon: There’s nothing to forgive, my lord.
Glover: There will be more fights to come. House Glover will stand behind House Stark as we have for a thousands years. And I will stand behind Jon Snow… the King in the North! The King in the North!
Game of Thrones, Season 6 Episode 10, "The Winds of Winter"