Depending on your implementation, you could have multiple rules triggered...
Some people use multiple rules to set the different dimensions, then have one final rule that sends the beacon....
However, if you aren't using that, and know that send beacons are always paired with set variables within your rules... while I don't know of any automatic way to pull this data... you could easily add to your "set variables" portion of your rules, a prop that is hard coded to a value (that indicates the rule name)...
This will require that your team is aware that if they copy rule and make modifications, they will need to manually edit the value of the prop. If the rule name is changed, they should also update this hard coded value.
I did also find this, but I have never tested it: https://experienceleague.adobe.com/docs/experience-platform/tags/client-side/satellite-object.html?lang=en
Under "Debugging Functions", I see some code to read the event.rule
You could try writing some custom JS in your rules custom code area to try and using these debugging options to populate a prop with the value (rather than logging it to the console).
If you are familiar with Javascript Coding, with some trial and error you can probably get something working... or ask your developers to help.... if those options don't work.. the manual process is the safest option, but like all manual processes, it's highly reliant on people following that process and it's subject to human error.