the date picker element should take the name you enter in the wizard, sometimes Dreamweaver wont recognize the name change unless you tab off the name after entering it.
if you need to change it after the fact, you can edit the name attribute of the form element in the code:
<input id="datepicker_1" name="mydatepicker" type="text" />
leave the ID as datepicker_x, but the name can be any valid form element name.