Sorry to disillusion you, but Waverly doesn't mean "quaking aspen." It's an old surname referring to a location in England.
In my opinion it's not a nature name. It's a popular culture name, now.
I don't like it because it makes me think of someone who is hesitant, trembling, can't make up their mind (wavering).
I'd expect Waverly to be a girl because the name reminds me of
Beverly and
Kimberly. And
Amberly.
I think it'd be alright as a middle name. Something naturey would be good.
June Waverly, maybe.
Azalea Waverly.
- mirfak