dimension
rk | 1_nm | 2_rk | 2_nm | 2_parent_rk | 3_rk | 3_nm | 3_parent_rk

1    one     -     -        -            -      -        -
2    two     -     -        -            -      -        -
3     -       3    three    1            -      -        -
4     -       4    four     1            -      -        -
5     -       5    five     2            -      -        -
6     -       6    six      2            -      -        -
7     -       -     -       -            7      seven    3
8     -       -     -       -            8      eight    3
9     -       -     -       -            9      nine     5

rk  | 1_nm |   2_nm        |   3_nm
1     one     -                -
2     two     -                -
3     one     one three        -
4     one     one four         -
5     two     two five         -
6     two     two six          -
7     one     one three     one three seven
8     one     one three     one three eight
9     two     two five      two five nine

proc sql noprint;
create table dim as
select *
from dimension;
quit;

proc sql noprint;
update dimension
set 1_nm = (select tbl.1_nm from dim as tbl where dimension.2_parent_rk eq tbl.rk);
quit;