Luna is an older name (it's a Roman goddess) but it's not timeless in the way that names like Tom or Elizabeth are - timeless generally means that they have remained roughly stable in popularity over a long period of time, which Luna hasn't, it's become very popular recently, which is what classifies it as a trend name.
It likely is the Harry Potter connection as well as it being an older and less widely used name in general which has caused that trend. Basically it's likely that in the future, you'll hear of a Luna and you'll think "She was born between 2010-2025" in the same way that a lot of babies were named Sarah and David in the 1980s.
I think the pet name boom happens when people like a name enough that they want to use it but they consider it a bit too out-there for their child. Luna walks a thin line here where some people think it's fine for a person (I would have used it if I'd had a daughter!) but some people don't, which is why it's currently popular for pets and babies.
This is interesting if you want to read about different name patterns. There's a UK version of this tool too.
https://waitbutwhy.com/2013/12/how-to-name-baby.html
How to Name a Baby — Wait But Why
Meet the Name Fad. In 30 years, the names Natalie, Chelsea, Samantha, and Lindsay will sound how Nancy, Cheryl, Susan, and Linda do today. And in 60 years, the names Ethan, Cody, Brandon, and Matthew will be Earl, Chester, Bernard, and Melvin.
https://waitbutwhy.com/2013/12/how-to-name-baby.html