The idea that each child in a family grows up in a unique environment is referred to as nonshared environmental effect
familial environmental effect.
niche-picking effect.
parent-child effect

Explanation:

Summary One of the most important findings that has emerged from human behavioral genetics involves the environment rather than heredity, providing the best available evidence for the importance of environmental influences on personality, psychopathology, and cognition. The research also converges on the remarkable conclusion that these environmental influences make two children in the same family as different from one another as are pairs of children selected randomly from the population.

The theme of the target article is that environmental differences between children in the same family (called “nonshared environment”) represent the major source of environmental variance for personality, psychopathology, and cognitive abilities. One example of the evidence that supports this conclusion involves correlations for pairs of adopted children reared in the same family from early in life. Because these children share family environment but not heredity, their correlation directly estimates the importance of shared family environment. For most psychological characteristics, correlations for adoptive “siblings” hover near zero, which implies that the relevant environmental influences are not shared by children in the same family. Although it has been thought that cognitive abilities represent an exception to this rule, recent data suggest that environmental variance that affects IQ is also of the nonshared variety after adolescence.