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.