I [name_u]LOVE[/name_u] [name_f]Posy[/name_f] and love that you will be using it! I would not use [name_u]Auburn[/name_u] myself because I do think it’s the kind of name best used if you have a real reason to, like the school or a surname (also: I’m a redhead, so NO!).
[name_f]Elizabeth[/name_f] is a versatile classic and I like it paired with more uncommon names, but something about [name_f]Caroline[/name_f] sounds so sweet and southern that I just like it a tad more.
Either way, I THINK I prefer the longer name ([name_f]Elizabeth[/name_f] or [name_f]Caroline[/name_f]) to follow [name_u]Auburn[/name_u] so you don’t have two two-syllable names in a row. But it sounds good either way! And maybe your last name makes a difference in how it sounds.