Does this help? It is not clear to me.
Push change code button instead of register.
Code:
Private Sub CommandButton2_Click()
Set ws = Worksheets("Register")
Lr = ws.Cells(Rows.Count, 2).End(xlUp).Row
With ws
.Range("B" & Lr) = TextBox1.Value
If TextBox2.Value <> "" Then .Range("C" & Lr) = TextBox2.Value
End With
Unload Me
End Sub