Howdy, and welcome to the board.
Here is one way to do it. I added a fourth column (D on the attached), named it NameLU and put into cell D2 this formula:
=A2&B2
Then I used five named ranges:
NameList
=OFFSET(Sheet1!$A$2,0,0,COUNTA(Sheet1!$A:$A)-1,1)
ChildList
=OFFSET(NameList,0,1)
NameList
=OFFSET(NameList,0,2)
NameLU
=OFFSET(NameList,0,3)
NameArray
=OFFSET(Sheet1!$A$2,0,0,COUNTA(Sheet1!$A:$A)-1,3)
With the new names in Column F, and Child 1 in G, etc., I put John in F2, and in G2 this formula:
=INDEX(NameArray,MATCH($F2&G$1,NameLU,FALSE),3)
Copy across and down as needed. This allows you to add as many names in columns A:C, and still work.
HTH