Some ISPs and contracts tie you to one number. If this applies and you have changed your number you must inform your ISP of the new number. Whether the new number is ex-directory or not is irrelevant.
If the new number is 'witheld' (this will not have been done unless you requested it), you will then have to prefix the access number with '1470' to release the number to your ISP.
Caller Line Identification applies to incoming calls on your line. If enabled, a Caller Display will show the number calling before you answer.
If you want to withold your number when making a call, dial 141 before the number.