Name History Affiliates

Why, of all things, did I choose My only one? Well, mostly because two of my favourite songs have "Only One" in their titles, and both could be used to describe different aspects of the relationship between the two.
The one that really gave me the idea was Only One by Yellowcard, and this part in the song:

I feel so broken up, and I give up.
I just want to tell you so you know:

Here I go, scream my lungs out and try to get to you,
You are my only one.
I let go, but there's just no one that gets me like you do,
You are my only, my only one.

It just makes me think about how, while they seem to be trying to forget about each other, they really can't move on. The song seems like it would be mainly from Davy's point of view though, because he seemed the most hurt by their betrayals.

The other song, however, is much happier - You're The Only One by Maria Mena, and only one part seems to work there:

And you're the only one who knows exactly what I mean.

This has turned into more of a music discussion than a name explanation.