PID Name
 0  P1
 1  P1
 1  P3
 0  P4
 0  P5
 1  P5

0 P1
 1 P3
 0 P4
 0 P5

var results = collection
               .Where(item => item.PID == 0 || item.PID == 1)
               .GroupBy(item => item.Name)
               .Select(g => g.OrderBy(item => item.PID).First());