ArrayList.remove is not working in a loop

You can use name.removeAll(Arrays.asList("Meg")); to remove all "Meg"

Your complete code would be

for ( int i = 0;  i < name.size(); i++){
    String oldName = name.get(i);
    if(oldName.equals("Meg"))
    {
       name.removeAll(Arrays.asList("Meg"));
    }
}

When you remove the first "Meg", the index i=2. Then it's incremented, but since one of the "Meg" is already removed, now name.get(3) is "Brain". So you didn't actually check the second "Meg".

To fix the problem. you can decrement the index when you remove an element:

public class ArrayListExp{
    public static void main (String[] args){

        ArrayList<String> name = new ArrayList<String>();

        name.add("Chris");
        name.add("Lois");
        name.add("Meg");
        name.add("Meg");
        name.add("Brain");
        name.add("Peter");
        name.add("Stewie");

        System.out.println(name);

        for ( int i = 0;  i < name.size(); i++){
            String oldName = name.get(i);
            if(oldName.equals("Meg"))
            {
                name.remove(i);
                i--;
            }
        }

        System.out.println(name);
    }
}

You're removing from the ArrayList while iterating over it from 0 to N, so when you remove the first Meg at index N, the next Meg moves down to index N, then you increment i to N+1. So the 2nd Meg doesn't get removed. Try iterating in the opposite order (N to 0):

for ( int i = name.size() - 1;  i >= 0; i--) {

You are iterating over the first Meg, and when that Meg gets removed, the array values shift over by one.

[Chris, Lois, Meg, Meg, Brain, Peter, Stewie]
   0     1     2    3     4      5       6

First Meg gets removed, and the loop increments i because it finished executing everything inside the for loop, so i will now be 3 and the array has been modified:

[Chris, Lois, Meg, Brain, Peter, Stewie]
   0     1     2     3      4      5      

Try iterating backwards.

for ( int i = name.size() - 1;  i >= 0; i--){
    String oldName = name.get(i);
    if(oldName.equals("Meg"))
    {
        name.remove(i);
    }
}