How to do partial match between two columns that contains names

Try this in E9.

=LET(
  a,FILTER(A9:B100,A9:A100<>""),
  MAP(INDEX(a,,1),LAMBDA(z,
    LET(
      b,TEXTSPLIT(SUBSTITUTE(SUBSTITUTE(z,"(",""),")",""),", ",,1),
      c,MAX(MMULT(--ISNUMBER(SEARCH(b,INDEX(a,,2))),    (SEQUENCE(COLUMNS(b)))^0)*1000+SEQUENCE(ROWS(INDEX(a,,1)))),
  INDEX(a,MOD(c,1000),1)
    )
  ))
)