Where does “Θαλία” come from?

Θαλία (Ancient Greek) comes from Ancient Greek θάλλω, from Proto-Indo-European dʰelh₁- — blossom; be green; to bloom, be green.

Ancestry of “Θαλία”, step by step

Step	Language	Word	Meaning
1	Ancient Greek	θάλλω	to bloom, sprout; to grow, flourish, thrive; to...
2	Proto-Indo-European	dʰelh₁-	blossom; be green; to bloom, be green