In Sword and Shield, there's a new feature associated with ribbons: you have the ability to select one ribbon as a "favorite" (alternatively, certain Pokemon known as Brilliant Pokemon will spawn with something called a Mark that has equivalent status to a ribbon, and you can set that mark as a favorite too). Each ribbon or mark has an honorary title associated with it, which appears after the nickname every time you send that Pokemon out from then on.
In your case, "the Once Well-Trained" is the title associated with the Effort Ribbon, which is obtained by maxing out the global budget of EVs. You can see a full list of ribbons, and their associated titles when you select each of them as a favorite, here.
