Call your telephone provider to set up your change of phone number and a specific date for the change to take place. You can find the number for your phone company on your bill. The phone company will take care of swapping your phone number and you need to contact your alarm company and city officials.
Notify your alarm company in writing that you are changing your phone number and tell them when the change takes place. Call the alarm company prior to the number changing to verify that they received your written notice. They will update your records and contact info.
Contact your city to notify them of your change of address if you are required to have a permit for your alarm system. You can probably find the forms online on your state's website, depending on your state. Fill them out and either email, mail, or fax them to the number or address on the form.