I took a pause from Subeta for a bit, Legacy Names were being implemented when I was last active. I created a new pet with a unique name (not in circulation currently). Do new pets get the Legacy tag for their names if it is unique or no?

No, only pets that were named before the change get the tag.

Darn, so if I give my pet a unique name there's nothing to differentiate it if someone else makes a pet with the same name anymore?

Unfortunately not. :(

Thank you for the info! :3