If we enrolled VM for OS monitoring and domain got changed for the same VM after few days then, will this OS monitors continue as it is or any issue can occur?
As far as LM is concerned, the identity of the server is tied to the IP address that the Collector uses to monitor it. You can change a lot of things about the device, but as long as the device IP address stays the same, LM will consider it the same device. Discovery will eventually run on the device after you make the change, potentially causing some instances/DataSources to disappear since they no longer apply, and new ones may show up. Depends on the change you make to the device.
There are only two things to consider here: reachability and authentication. Unless you're changing the IP address or the network in some way, reachability is unaffected. Authentication is the only thing to keep in mind here. Your Collector defaults to using integrated authentication, meaning that the credentials used to run the Collector service are used to communicate with remote devices. In this case, if some target servers are moved to another domain, you'll need to make sure that the credentials used to run the Collector service still have the requisite permission on those systems in the new domain. This can be accomplished, like @Mike Moniz mentioned, using a trust between the two domains.
The other way authentication can happen is if you specify the Windows credentials as properties on the devices in LM. If you do this, the Collector uses those credentials instead of the integrated credentials for access to remote systems.
Look at these two support documents: https://www.logicmonitor.com/support/getting-started/advanced-logicmonitor-setup/defining-authentication-credentials and https://www.logicmonitor.com/support/getting-started/advanced-logicmonitor-setup/credentials-for-accessing-remote-windows-computers/
