c# How to get from a Json string to class instance then calling method

I have a (sql) table with these entries:

Table:

Type (varchar)     Json (varchar)
MyClassA           { "Id": 1, "Name": "OneName" }   
MyClassB           { "Id": 2, "Name": "TwoName" }

I need to call a method in ClassA and/or ClassB to change the Name property.

Something like the next code:

public void Test(string type, string json)
{
   Type type = Type.GetType($"MyNamespace.a.b.{type}, MyDll");

   // Some code here....
   // - Casting to IData    ??
   // - var obj = JsonConvert.DeserializeObject(json);       ??
   // - var obj = JsonConectt.DeserializeObject<type>(json)  ??
   // - var x = Convert.Change(...) ??


   instance.DoSomething("bazinga");

}


public interface IData 
{
   void DoSomething();
}

public class MyClassA : IData
{
   public int Id {get; set;}
   public string Name {get; set;}

   public void DoSomething(string newName)
   {
       Name = newName;
   }
}

public class MyClassB : IData
{
   public int Id {get; set;}
   public string Name {get; set;}

   public void DoSomething(string newName)
   {
       name = $"{Id}, {newName}";
   }
}

Attempt A:

var obj = JsonConvert.DeserializeObject(json);
var ins = obj as IData;
// ins = null

Attempt B:

dynamic obj = JsonConvert.DeserializeObject<dynamic>(json);
// failed

Attempt C:

var obj = JsonConvert.DeseriallizeObject<type>(json);
// Not allowed to use 'type' in this way.