With the exception of Fresh, Magic User, and Healin' Good, these Cure name has another meaning, which alludes to their powers.
-Even though this became a thing with Yes! 5, it's sequel marks their return as indestructable, the names might've dropped somehow. Unless you count the title for Rose's attack, indicating she's an ally than a Cure.
-Fresh loosely doesn't need to follow this trait
-Heartcatch use these for their sub attacks
-Suite need to follow this, except for Beat
-Smile all part of the brand
-Doki Doki follow up on this as well
-Happiness Charge use these for their sub attacks, like Heartcatch
-Go! Princess, not as much, for Scarlet, she's got other names (don't expect I missed, ''Floral,'' because they switched gears entirely)
-Magic User is about focusing on magic
-Sparkling A La Mode demands it
-Hug! Heart doesn't do much, except for Macherie & Amour
-Star Twinkle, yes
-Healin' Goods focus on the teamwork with their partners
-Tropical Rouge, yes
-Delicious Party, yes
-Soaring Sky, definitely, well, except Majesty
-Wonderful, too much focus
-You and Idol, absolutely