Big O of list resize

This question applies to all languages but let me stick to C#

var names = new List<string> {"Jerry", "Cosmo", "Elaine", "George"};

This is my compile time list. If I decide to insert record into it, then .Net underneath doubles the length from 4 to 8.

names.Insert("Newman");

Does Big-O of this insert method above become O(N)? Where N as length of the list? If yes, do most interviewers really care?

EDIT

Lets say we are inserting 1000 records.. Length will double at 4, 8, 16, 32.... So insert complexity will be Log(N) correct?