Yes, send your companions out to spread your word. You just have to talk to them then select the "I would like to ask you something" option then the "you know I would like to be king option". They will support you and give you a piece of advice about ruling your faction related to their background. Some pieces of advice clash however, so if you accept one you may not be able to send another.
I've sent out everyone of my companians to spread word of my awesomeness, They all say different things that they think will get you into power like a long lost ancestor who was an emperor or marks on your hands. Some companions will disagree with other companions missions to raise support but generally just send them all out You lose RTR on failing quests also, You gain it if you have a lot of prisoners in your party/fiefs when the truce comes as well