Solution

25240

First name
Sam
School
Lawrence Sheriff
Country
Age
16

At least it seems that the lowest that this can be done in is eight, all shared between them:

Naomi and Alex share 1; Alex and Chris share 2; Chris and Alex share 3; Naomi and Chris share 2 and they all share 2 in the centre.

Naomi gets 1+2+2 = 5
Alex gets 1+2+3 = 6
Chris gets 2+2+3 = 7

I have proved it, not formally however.