Does the node replication use the same policy name of the source node to establish the target node? Does the source policy content have to match the target policy's content in terms of management classes etc.?

It is not required to have same policies, however, it is recommended and considered best practice that the policies on the source and target servers are configured the same.

Check following for more detail..

https://www.ibm.com/support/knowledgecenter/en/SSGSG7_7.1.1/com.ibm.itsm.srv.doc/c_repl_policy.html