My GF and I play in our local APA league, and play in both an 8 ball, and a 9 ball division. We're the ones that give out the patches to whoever gets them for those two divisions. They really are a big deal for people when they first start playing, and for when someone beats a higher level handicap person in the league.
In our league, any patches earned in a match get communicated to the League Operator through the scoring app. There is a "comments" section, at the final stage of submitting the match results in the app, where those achievements would get noted. The league operator then compiles the patches earned, and forwards a list to us. My girl then puts whatever patches are earned into little baggies for each team, with a note as to who gets what, and will give them out to those teams when we play them. She also brings her box of patches to our weekly matches, and if someone earns one while playing our team, they get the patch right away. We call that "insta-patch". Every now and then, someone will remember a patch that they should have earned, and with the scoring app, most can be documented within the app, so they'll get that patch then too. We went a long time when no patches were distributed under a previous LO, so our new one made it a point to correct that, and my GF has really taken to . She does a great job of making sure anyone that earns one, gets it.