Get the Entity Name when calling SaveChanges in Entity Framework 6.1.3

You need to override SaveChanges method of DbContext and use ChangeTracker to track the changes made to entities before it gets saved to database.public

public class ChangeLog  
{
    public string EntityName { get; set; }
    public string PropertyName { get; set; }
    public string OldValue { get; set; }
    public string NewValue { get; set; }
}

public override int SaveChanges()  
{
    var modifiedEntities = ChangeTracker.Entries()
        .Where(p => p.State == EntityState.Modified).ToList();

    foreach (var change in modifiedEntities)
    {
        var entityName = change.Entity.GetType().Name;

        foreach(var prop in change.OriginalValues.PropertyNames)
        {
            var originalValue = change.OriginalValues[prop].ToString();
            var currentValue = change.CurrentValues[prop].ToString();
            if (originalValue != currentValue)
            {
                ChangeLog log = new ChangeLog()
                {
                    EntityName = entityName,
                    PropertyName = prop,
                    OldValue = originalValue,
                    NewValue = currentValue,
                };
                ChangeLogs.Add(log);
            }
        }
    }        
    return base.SaveChanges();
}

In above snippet we have queried change tracker api to fetch the entities that are modified

var modifiedEntities = ChangeTracker.Entries()
        .Where(p => p.State == EntityState.Modified).ToList();

Same way you can query entities that are added and deleted.

Edit

object GetPrimaryKeyValue(DbEntityEntry entry)  
{
        var stateEntry = ((IObjectContextAdapter)this).ObjectContext.ObjectStateManager.GetObjectStateEntry(entry.Entity);
        return stateEntry.EntityKey.EntityKeyValues[0].Value;
}

Note: If you have Identity Insert set to On then for added entity above snippet will not work.