You can use the label.Name property to change the name of any label.
It doesn't rename the declaration of the variable, for that you'll need to use find/replace.
Example from MSDN help:
Private Sub Form1_Load(ByVal sender As Object, ByVal e As System.EventArgs) Handles MyBase.Load
' Connect the ControlRemoved and ControlAdded event handlers to the event-handler methods.
' ControlRemoved and ControlAdded are not available at design time.
AddHandler Me.ControlRemoved, AddressOf Me.Control_Removed
AddHandler Me.ControlAdded, AddressOf Me.Control_Added
End Sub 'Form1_Load
Private Sub Control_Added(ByVal sender As Object, ByVal e As System.Windows.Forms.ControlEventArgs)
MessageBox.Show(("The control named " + e.Control.Name + " has been added to the form."))
End Sub
Private Sub Control_Removed(ByVal sender As Object, ByVal e As System.Windows.Forms.ControlEventArgs)
MessageBox.Show(("The control named " + e.Control.Name + " has been removed from the form."))
End Sub
' Click event handler for a Button control. Adds a TextBox to the form.
Private Sub addControl_Click(ByVal sender As Object, ByVal e As System.EventArgs) Handles button1.Click
' Create a new TextBox control and add it to the form.
Dim textBox1 As New TextBox()
textBox1.Size = New Size(100, 10)
textBox1.Location = New Point(10, 10)
' Name the control in order to remove it later.
' The name must be specified if a control is added at run time.
textBox1.Name = "textBox1"
' Add the control to the form's control collection.
Me.Controls.Add(textBox1)
End Sub
' Click event handler for a Button control.
' Removes the previously added TextBox from the form.
Private Sub removeControl_Click(ByVal sender As Object, ByVal e As System.EventArgs) Handles button2.Click
' Loop through all controls in the form's control collection.
Dim tempCtrl As Control
For Each tempCtrl In Me.Controls
' Determine whether the control is textBox1,
' and if it is, remove it.
If tempCtrl.Name = "textBox1" Then
Me.Controls.Remove(tempCtrl)
End If
Next tempCtrl
End Sub