It could be really cool if you where able to have a checkbox when you are creating Tags in triggers, so you can have your preferred labels / tags show as the first visible ones.

E.g. you are using the  ServiceNow Integration and you want to have the INC number as first value and maybe your OS tag aswell.

Maybe limit  to show 3 tags as maximum that has priority. maybe with hierarchy of overwrite/Priority  goes highest is Actions then Triggers then Hosts then Templates.

If you need a more information please let me know.