Firstly, that's a nasty bit of UI - clearing out everything because he made a minor slip is rather unpleasant, and second because it won't work as is.
If I type "A123345!"£$%^&*(" is will accept it, because it starts with a valid character.
You can fix it so it works and only accepts letters and spaces very easily:
if (!System.Text.RegularExpressions.Regex.IsMatch(textBox_Ansprechpartner_Name.Text, "^[a-zA-Z ]*$"))
But I'd look at saving the previous version:
private string lastEntry = "";
private void textBox_Ansprechpartner_Name_TextChanged(object sender, EventArgs e)
{
if (!System.Text.RegularExpressions.Regex.IsMatch(textBox_Ansprechpartner_Name.Text, "^[a-zA-Z ]*$"))
{
int loc = textBox_Ansprechpartner_Name.SelectionStart;
MessageBox.Show("This textbox may only contain letters.");
textBox_Ansprechpartner_Name.Text = lastEntry;
textBox_Ansprechpartner_Name.SelectionStart = loc;
}
lastEntry = textBox_Ansprechpartner_Name.Text;
}