I don't think it's too nickname like. I didn't think of Adela until I read the post. Dela might look like it's short for Adela, but Della looks complete on its own.
That's exactly what I thought. I never would've guessed that it came from Adela. I thought it was a name by itself. I like the idea of it being a variant of Adela though. That way, it still means "noble". I think it looks complete too.