Will changing Salesforce Domain affect the Campaign Monitor integration?

In most cases, no action is required. The integration relies on your Salesforce Org ID, not the domain name, to manage licenses and access — so a domain name change alone will not break the connection. 

However, in rare cases, the domain update might cause the connection to Campaign Monitor to drop. If that happens, simply reconnect to Campaign Monitor via the setup page. All of your sync settings and data will remain intact after reconnecting.

You can follow the reconnection steps here: How can I change the sync user in Campaign Monitor?