This is a song written by cowboy star Eddie Dean.  He also wrote
Hillbilly heaven

One has my name

[G]One has my name, the [D7]other has my heart.
    With one I'll remain, that's [G]how my heartaches start
One has brown eyes, the [C]other's eyes are blue
    To [A7]one I am tied, to the [D7]other I'll be true

[G]One has my love, the [D7]other only me
    But what good is love to a [G]heart that can't be free
If I could live over my [C]life, I would change
    The [G]one who has my heart would [D7]also have my [G]name