You can use a worksheet event under the worksheet that contains the cell.
Rightclick on the worksheet tab with the changing cell. Select view code.
Paste this into the newly opened code window:
Option Explicit
Private Sub Worksheet_Change(ByVal Target As Range)
Dim myCell As Range
Set myCell = Me.Range("A1")
If Target.Cells.Count > 1 Then
Exit Sub 'one cell at a time
End If
If Intersect(Target, myCell) Is Nothing Then
Exit Sub
End If
Worksheets("sheet1").CommandButton1.Caption _
= Format(myCell.Value, "mmmm dd, yyyy")
End Sub
You'll have to change the cell to look at (I used A1). As well as the other
worksheet's name, the commandbutton's name and use the caption you want.