several great artists recorded this, Don Gibson,  Jim Reeves, Carl
Smith, Jimmy Wakley, Hank Locklin..... to name a  few.
I preffer the  Hank Locklin version...... Here is how I play it....have fun
with  it

            One Has My Name, The Other Has My Heart

(A)One has my name, the (E) other has my  heart
With one I'll remain, Thats (A) when my heartaches  start
One has brown eyes, the (D) others eyes are  blue
To (A) one I am (E) Tied, but to the other I am (A)  true

(A) One has my love, the (E) other only  me
But what good is love to a (A) heart that cant be  free
So I'll go on living my (A7) life just the (D)  same,
While (A) one has my heart, and the (E) other has  my (A) name

********....instrumental break......2 lines...  ***********

(A) One has my love, The (E) other only  me
But what good is love to a (A) heart that cant be  free
If I could live over my (A7) life i would (D)  change
The (A) one who has my heart, would (E) also have  my (A) name