class User
{
    public int Id { get;set; }
    public string name { get;set; }
}

List<User> obsoleteUsers = olduser.Except(newuser).ToList();

class User : IEquatable<User> {
    public int Id { get; set; }
    public string name { get; set; }

    public bool Equals(User other) {
      if (null == other)
        return false;

      return
        Id == other.Id &&
        string.Equals(name, other.name, StringComparison.OrdinalIgnoreCase);
    }

    public override bool Equals(object obj) => Equals(obj as User);

    public override int GetHashCode() => Id;
  }

class UserNameComparer : IEqualityComparer<User>
{
    public UserNameComparer(StringComparer comparer)
    {
        if (Comparer == null) throw new ArgumentNullException(nameof(comparer));
        this.Comparer = comparer;
    }

    public StringComparer Comparer { get; }

    public bool Equals(User x, User y)
    {
        if (x == null || y == null) return true;
        return Comparer.Equals(x.name, y.name);
    }

    public int GetHashCode(User obj)
    {
        return Comparer.GetHashCode(obj?.name);
    }
}

List<User> obsoleteUsers = olduser
    .Except(newuser, new UserNameComparer(StringComparer.InvariantCultureIgnoreCase))
    .ToList();