I need to change my phone number for my account

You don't need a new password.

You need to change/add the number on your Apple ID. Look in the Security section when signed in online. You may have to add the new number before you can remove the old number. After the change, allow up to 24 hours for the change to sync. Before trying to make the change, sign out of Messages/FaceTime on all devices/computers.

Apple ID - Manage