Assuming that the button that was clicked still has the focus, use
   Screen.ActiveControl.Name
to get the name of the button.

One way to do this is to use the OpenArgs parameter of the form.  You can
send information from one form to another with this parameter.  So assuming
you have a button named Button1 (and I hope it's not) you can do this in its
OnClick event:

   stDocName = "customer2"
   DoCmd.OpenForm stDocName, , , , , , "Button1"

In the Customer2 form, you would read the OpenArgs string in the OnLoad
event and use it somehow.  For instance, you could set this value to the
caption of a label to display which button was pushed.  Something like this:

Private Sub Form_Load()
   Me.Label10.Caption = Nz(OpenArgs, "")
End Sub

This will cause the value "Button1" to appear in the label when the second
form is opened.

Note: I usually use the Nz function in case the form is opened without that
argument.  Under some circumstances (like if you were assigning the value to
a variable) a Null value in the OpenArgs will cause an Error.