My personal house rule for renown was actually to import ICON's handling of renown to CODA, specifically the breakdown of renown into different categories.
I don't have my notes at hand and it's been sadly a few years I have not gamed, but if I remember correctly, I ruled that 1 renown point in CODA was rougly 10 ICON renown points, and broken down into the ICON categories, which were something like Skill, Agression, Diplomacy, and one or two more I can't remember.
That way renown awards were a cool way to reward players for outstanding actions (good or bad), and to celebrate some particular moments at the gaming table.
For instance, I remember the Science Officer having to send an urgent report to Starfleet, but rolling a critical failure when gathering data... This led to the character gaining a negative renown in skill.
As for actual use of renown, it was not something automatic. Either the player decided to actively use it ("Do you know who I am ?"), or I wanted to spice things a little ("The Ferengi smiles crookedly and asks if you were not by any chance the same Starfleet Officer who was helped by his cousin Sniok"), but not every encounters led to automatic renown dice rolling.
"The main difference between Trekkies and Manchester United fans is that Trekkies never trashed a train carriage. So why are the Trekkies the social outcasts?"
Terry Pratchett