This is exactly the other way around. Global reputation is what enables you to unlock portraits - along with spending money. Each trader explicitly tells you how much reputation and how much money you need to unlock their next level.Answering my own question, it seems the global reputation rises every time you unlock a new portrait from a trader. And the different level of trader portrait might be your mileage for total money spent at that trader. In short go spend money at different traders.
Global reputation is raised by killing enemies - the higher the level of the enemy, the more reputation they give. At a certain point, killing lower level enemies will not give you any reputation.
EDIT: after more testing, it appears that I was partially incorrect - spending money at different traders does raise your reputation - however, it appears you need to travel to different traders, and spend a bit of money at each one. Meaning you can't dump all of your cash at one trader, and see a reputation spike.
Killing enemies also seems to raise your reputation, though the effects are more muted than I had thought.
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