I think of you often, and it makes me smile,
I haven't been this happy in a long long while,
right now we're just friends, and that's ok with me,
but I hope that one day you'll turn around and see,
that i'm right there behind you like I've been from the start,
waiting there patiently to give you my heart.
Depends on what genre the song is in.
If it's a acoustic/80's love song:

"Realize", "Waiting", "Until then" or something short.

If it's a metalcore/deathcore song maybe something like:

"Italian plumbers get all the women" or "Gandalf touched my special area"

(Also first post Yay!)
Girls don't want you hanging around them like a hungry cat, metaphorically or emotionally, as if you're waiting for them to finally make the right decision and be with you. Even if it's not a stance of arrogance, it still isn't reality, and certainly shouldn't be. I don't want my girl to turn around and find me there with my heart in my hand.

What have you said here that you cannot say in everyday life? Seriously, what have you offered that differentiates it from something you'd say to your best mate in a brief moment of emotion? Being realistic in terms of language is fine if it fits the theme - and if that theme is strong enough to hold its own - but you also have to do some tarting.

Tarting isn't about being pretentious or layering on foundation after mascara after lipstick - I'm not interested in fake tan - But you can still pretty yourself up so that it benefits yourself. Compliments can be given by yourself in all walks of life, including writing, not just fashion sense or grooming.

In this instance, I feel like you need to show me you're really keen on this woman. Like guitar playing, techniques can add emotion, dynamics and layers. Learn a few basic techniques, like alliteration, assonance, line-breaking, metaphors, similes, rhyming, internal rhyming, etc. Then start to implement those into your writing. You'll soon notice that your theme and thoughts coming alive without you even trying. It opens up a whole new world of emotion.
I'm not sure what kind of genre you're going for, but i think something like "From the Start" or "Waiting There" might be good.