Changing the value of an element in a list of structs

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Not quite. Designing a type as class or struct shouldn’t be driven by your need to store it in collections 🙂 You should look at the ‘semantics’ needed

The problem you’re seeing is due to value type semantics. Each value type variable/reference is a new instance. When you say 

Struct obItem = MyList[1];

what happens is that a new instance of the struct is created and all members are copied one by one. So that you have a clone of MyList[1] i.e. 2 instances.
Now if you modify obItem, it doesn’t affect the original.

obItem.Name = "Gishu";  // MyList[1].Name still remains "peter"

Now bear with me for 2 mins here (This takes a while to gulp down.. it did for me 🙂
If you really need structs to be stored in a collection and modified like you indicated in your question, you’ll have to make your struct expose an interface (However this will result in boxing). You can then modify the actual struct via an interface reference, which refers to the boxed object.

The following code snippet illustrates what I just said above

public interface IMyStructModifier
{
    String Name { set; }
}
public struct MyStruct : IMyStructModifier ...

List<Object> obList = new List<object>();
obList.Add(new MyStruct("ABC"));
obList.Add(new MyStruct("DEF"));

MyStruct temp = (MyStruct)obList[1];
temp.Name = "Gishu";
foreach (MyStruct s in obList) // => "ABC", "DEF"
{
    Console.WriteLine(s.Name);
}

IMyStructModifier temp2 = obList[1] as IMyStructModifier;
temp2.Name = "Now Gishu";
foreach (MyStruct s in obList) // => "ABC", "Now Gishu"
{
    Console.WriteLine(s.Name);
}

HTH. Good Question.
Update: @Hath – you had me running to check if I overlooked something that simple. (It would be inconsistent if setter properties dont and methods did – the .Net universe is still balanced 🙂
Setter method doesn’t work
obList2[1] returns a copy whose state would be modified. Original struct in list stays unmodified. So Set-via-Interface seems to be only way to do it.

List<MyStruct> obList2 = new List<MyStruct>();
obList2.Add(new MyStruct("ABC"));
obList2.Add(new MyStruct("DEF"));
obList2[1].SetName("WTH");
foreach (MyStruct s in obList2) // => "ABC", "DEF"
{
    Console.WriteLine(s.Name);
}

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