First off, names can contain anything: "John Henderson-Allan" is a valid name. So are "StopFortnumAndMasonFoieGras Cruelty.com" and "Brfxxccxxmnpcccclllmmnprxvclmnckssqlbb11116" - so you shouldn't ban anything in particular from a name, any more than you should ban any of these "!#$%&'*+-/=?^_`{|}~" from an email address.
But, to restrict a textbox to upper and lower case letters only just use a Regex:
Regex regex = new Regex("^[a-zA-Z]+$");
bool hasOnlyAlpha = regex.IsMatch(myTextBox.Text);