Gaining fame for your faction in Uncharted Waters is relatively easy, you can get fame in the following ways:
Killing monsters will not normally gain you faction, unless the monster is aligned with the opposing faction in which case it might.
Fame is needed to unlock titles (which get you better boats), it is also needed to gain rewards for your actions and as a way to rank yourself with your fellow players. Simply the more fame you have the better you are!
It is possible for low level players who just concentrate on getting fame to have more fame than higher level players who have concentrated on levelling, so it makes for a bit more fun and rivalry!