OK, that makes sense. He’s got a connection to the original, he’s got a right to the name, he’s got a legacy of magic, DC gets to keep the trademark going, etc.
But wait a minute. Like the original, Zatara’s his last name. Zatanna, however, is her first name. (Though I have to question the wisdom in naming your daughter “Zatanna Zatara,” “Zachary Zatara” isn’t much better. I wonder if they ever get together and perform with ZZ Top?)
We have two related characters, one male, one female. The teenage boy goes by his last name, and the grown woman goes by her first name.