The easiest way to change your number would be to contact the service provider and have it changed. Unfortunately, if you're using a traditional phone number and are communicating via SMS (which is what Viber does), your contacts won't be able to chat with you without the new number.
My suggestion is to maybe to switch over from a telephone-based chat app to a web-based chat app if you're looking to change contact forms without the use of a telephone number.