I assume taking cabal items & killing cabal members makes your reknown lower (but conversely may also be raising it in another) against that member's cabal and raising your own in your cabal. But if it's not a target of yours, i.e. battle char killing random uncaballed warriors for fun, I'd assume he is not raising his reknown probably by killing them. It's not just a PK tally, it's a gauge of your char's actions in relation to each cabal's ideologies.

The hardest one to raise I've found to be herald

Helping people retrieve their item looks to raise your reknown with them.

Take a battle char as an example.
He can probably raise his battle reknown by
Killing nexus char
Killing scion char
Killing any mage
Raiding Scion
Raiding Nexus
Retrieving the head
Giving items to Tahren

Those actions will also likely make him more hated by nexus/scion/whatever cabal random mage is in.

Keep in mind though, killing a scion might also raise your reknown in fort because a scion is an enemy of both cabals.
Not sure just how simple or complex it is, you'd have to ask Zulg, but generally if you are caballed and following cabal rules, you'll end up maxing it out in your cabal pretty easily.

I believe with my nexus leader, I maxed out nexus and almost fort as well, and was hated by battle only.

With my battle leader I was hated by scion/nexus/and I think trib, neutral or disliked by outlander/herald/fort, and reknowned in Battle.

But you can use it at level 1 to get a feel. A wood elf has a naturally higher reknown in outlander, so is may be friendly, while a dwarf starts off disliked by Outlander as he is a natural enemy. Goodies have an affinity for fort, and so on.

It's an interesting tool, one most players probably don't use, or don't even know about. I could see it as useful for cabal leaders to see the reknown of their members though.