Ciao
Puoi usare i metodi del namespace Globalization, in particolare la classe TextInfo e la funzione ToTitleCase():
Dim before As String() = New String() {"nome cognome", "prova con 'apostrofo", "pippo PLUTO"}
Dim after As String() = New String(before.Length - 1) {}
Dim ita As TextInfo = CultureInfo.GetCultureInfo("it", "it").TextInfo
For i As Integer = 0 To before.Length - 1
after(i) = ita.ToTitleCase(before(i).ToLower)
Next i
Dim sb As New StringBuilder()
For i As Integer = 0 To after.Length - 1
sb.Append(before(i))
sb.Append(" --> ")
sb.AppendLine(after(i))
Next i
MessageBox.Show(sb.ToString)
Luca