
Huevember – Day 28.

Huevember – Day 14.
“And they told how afterward Ned had carried Ser Arthur’s sword back to the beautiful young sister who awaited him in a castle called Starfall on the shores of the Summer Sea. The Lady Ashara Dayne, tall and fair, with haunting violet eyes.”
( A Game of Thrones – Catelyn II )

Huevember – Day 2.
“Must!” She put her hand on his good leg, just above the knee. “A true man does what he will, not what he must.” Her fingers brushed lightly against his thigh, the gentlest of promises. ( A Game of Thrones – Eddard
XII )
Because Jon Arryn was a beloved father-figure (especially with Rickard dead) and Ned wanted to honor him. I don’t think it was a political motivation at all.
Promise me, Ned, Lyanna pleaded, and Jon’s name is that promise. Jon Arryn was a beloved father-figure who took Ned under his protection, and went to war when the king called for his head. In a single name Ned promises to be a father to Jon Snow the same way Jon Arryn was a father to him, to raise him, protect him, and defy the crown for him if need be. If Robert ever found out, Ned was choosing Jon.
asoiaf meme [2/4] quotes –
“My aunt Allyria says Lady Ashara and your father fell in love at Harrenhal – “
“That’s not so. He loved my lady mother.“
“I’m sure he did, my lady, but – “
“She was the only one he loved.”