It's kind of interesting in that they were generally... simpler. In a way, truer to the Japanese ones (that are mostly really simple).

However they figured they seemed too generic. As in, generic RPG monster name; what you'd see in a traditional fantasy game:

Nagaasp drew near!
Dragyn cast Blizzard! It inflicted extreme damage to Parasyte!

Because they figured they wanted to go a different route, with the monsters closer to the players, they decided to think up different names that reflected this.

Some are still pretty neat though. "Nagaasp" is much better than Arbok any day. (Naga, serpent deities, and Asp, a kind of snake, over... Cobra backwards with a k)

Finally, Dragoon and Dragyn...I still don't know exactly how these names would have worked.

The extremely overused and generic "Dragoon" for which a quick search of the word will give you about five different franchises... does fit Dratini as it also comes from the "dragons associated with lagoons" myth.
Dragyn... might be from Dragon+Wyvern or something. Still, it's another generic dragon name.