This error can occur during replica creation (using either the CreateReplica or CreateReplicaFromServer tool) if the Replica Name parameter conflicts with a replica name that exists in either the source or destination geodatabase. Each replica name must be unique to the user creating it. User1 and user2 could each create a replica called MyReplica, but neither could create multiple replicas with that name.
To solve this, simply change the value of the Replica Name parameter so that it doesn't conflict with an existing replica owned by the connected user. For local geodatabases, you can use the replica manager to get a list of the replicas in a geodatabase. If accessing remote geodatabases via ArcGIS Server, the best solution is to specify a new name for your replica. See Creating replicas for more information.