Yes you can, but if it's due to nuisance calls we'd advise you to let us know so we can investigate it further.
If they are Premium Rate Services, you can stop them by texting "STOP" to the shortcode number of these services.
Alternatively, please contact an agent. Select the categories "Mobile Services" and then "Preventing unwanted calls". Select "Incoming" and give us details about the calls you are receiving.
If you just want to change your number, with effect from April 2015, there are two methods. Before you start note that whichever method you choose you will be allocated a random number. If you want to choose your number or want a memorable number, you need to purchase one elsewhere and transfer (port) it to giffgaff.