One Has My Name (The Other Has My Heart)
Jerry Wallace
Written by Eddie Dean, Lorene Dean, and Hal Blair
Wallace's version not released as a single but Barry Young put it on the Pop chart
  at # 13 in 1966
Additionally, found on Country chart in 1948 by Jimmy Wakely (#1) and Eddie 
Dean (#11); in 1949 by Bob Eberly at # 8; and in 1969 by Jerry Lee Lewis at #3.

One has my name, the other has my heart
With one I'll remain, that's how my heartaches start
One has brown eyes, the other's eyes are blue
To one I am tied, to the other I am true

One has my love, the other only me
But what good is love to a heart that can't be free?
So I'll go on livin' my life just the same
While one has my heart, the other has my name

<instrumental first two lines>
One has brown eyes, the other's eyes are blue
To one I am tied, to the other I am true

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