The Mormonts of Bear Islands has been loyal to the Starks which we come to know in Season 5. When Stannis Baratheon asked them to pledge fealty to him. A raven sent by Lady Lyanna Mormont carried a letter that announced her refusal saying, "Bear Island knows no king but the King in the North, whose name is STARK ".
Later, in Season 6 Jon Snow and Sansa Stark visited her to ask for her support when they march to the North against the Boltons. Sansa tried to flatter her and said you were named after my aunt Lyanna.
Why was she named after Lyanna Stark?