All the logging is handled by a third party library and even if that were not the case, you couldn’t override anything like that from a rule. And there isn’t one logger per Item. It’s one logger for everything that gets put on the event bus.
But, Frontail has a filter option and you can filter the logs you are seeing down to just those lines you care about at the time. For example (MyItem1|MyItem2) as the filter will only show those lines containing those two Item names.
If on the command line see How to watch and look through logging where you can filter out those lines that match those Items you don’t care about.
In OH3 the Developer Sidebar will show the same information from events.log and you can filter that down to just the Items you want to see.
Or you can set the logs to permanently (until reconfigured) to exclude log statements that match a regular expression from being logged out. See openHAB - Filtering event logs, though that post needs to be updated for OH3’s log4j2.xml formatting.