Dalvin was intrigued by this proposition. A special name for Ling Long was an endearing idea and could further cement their relationship positively, so he seriously began to ponder upon the available options.
The 'Dao Lin' he used was just a play on his name, Dalvin, due to it being mispronounced in the language of the denizens of Tianzi due to their accent. After all, English was not a thing here, so they were all speaking the native language of Tianzi.
The Dao Lin itself was something he kept because he liked what it meant. The version of the name that Lao Li had mispronounced was of a different meaning, being 'Dao' for arrival or 'to arrive' and 'Lin' as in forest or the woods.
As you could imagine, this was a fitting name that even Lao Li thought was appropriate given Dalvin's wood element abilities and Dalvin himself accepted it at the time because it really did sound fitting.