How To Auto Run Macro On Cell Change

I'm trying to automatically change the names of the sheets in my workbook based on the contents of cell A1 in each sheet.

I found some code on some website and inserted it into the ThisWorksheet module:

Code:
Private Sub Workbook_Open()
Dim wSheet As Worksheet
On Error Resume Next
For Each wSheet In Me.Worksheets
if wSheet.Name = "SomeName" then
If wSheet.Range("A1") = "" Then
wSheet.Name = "Sheet" & wSheet.Index

[code].....

This code appears to work properly, but only when the workbook is closed and then reopened. Is there a way to make this code run anytime cell A1 in any of the sheets changes? I've found several sample codes that purport to make a macro run automatically on a cell change, but I can't figure out how to incorporate the code above with the Worksheet_Change code to make them work together.