Generally speaking - most hosting providers allow custom nameservers to be set so changing your hosting service provider is not normally a problem. To keep Ezoic running during and after the switch, you'll need to update your IP address in your Ezoic Dashboard. You can do this by logging into your account here and navigating to Settings > Advanced > DNS Settings. You'll want to update the IP address to the location of your new host. Press save and you're good to go. 

It may be a good idea to keep your Ezoic representative informed of when you plan to make the switch so that they can help you if any problems arise. 

On the other hand, some hosting companies place conditions such as requiring the domain name to be registered with the same company. In very rare cases a hosting company will not provide the facility to have customized nameservers - in these cases you will not be able to move to that hosting company and remain with Ezoic.

Most hosting companies make the switch fairly easy through the hosting company's cpanel or user interface. If you are experiencing difficulty finding this give Ezoic support a shout ( and we'll point you in the right direction!