I think it would actually be easier and less confusing to give each class it's own set of names for ability types, and only copy names when you copy mechanics as well. Because at the end of the day, a player only needs to understand one class at a time.
It might look like more work on the part of the dm, but most dms can and do lean on player to know their own stuff. Those of us who dig in will see the patterns, but that's only really useful when you're looking to homebrew new content - something that doesn't need to be obvious.
Well that's how it would look anyway.
The Babarbian only one with Rages by default. The Fighter would be the Manuever user. The Monk would have Martial Arts. etc. The default would mostly attach one power/feature type to a single or pair of classes. Only a few of them would break the rules likehow their wouldbe several spell users. Or how Wizards have Cantrips, Spells, and Rituals.
Only later via variants, DM houserules, and future books would they really combine. When Xanatar's 2 comes out with the Kensei that uses Martial Arts and Manuevers or a Swashbuckler with Maneuvers and Tricks, then a player would have to truly know both.