Textbox will not help you to it as it supports only plain text, you need to use Rich Textbox control so that you can achieve what you get.
see below snippet
richTextBox1.SelectionFont = new Font("Times New Roman", 10, FontStyle.Underline);
richTextBox1.SelectedText = "Message:";
richTextBox1.SelectionFont = new Font("Times New Roman", 10, FontStyle.Regular);
richTextBox1.SelectedText = " This is a message for Name of Client.";