If you need to change a remote connection URL, you first need the connection ID. The API returns it when you first create the connection but you can also get it later by listing the connections for a given view:

query {
  searchDomain(name: "myMultiClusterView") {
    ... on View {
      remoteConnections {
        id
        ... on RemoteClusterConnection {
          publicUrl
        }
      }
    }
  }
}

This will return something that looks like this:

{
  "data": {
    "searchDomain": {
      "remoteConnections": [
        {
          "id": "CW8ppOz5CUfabsT7zB5dKIRs05DqIHuR",
          "publicUrl": "https://remotelogscale.com/"
        }
      ]
    }
  }
}

The connection ID is CW8ppOz5CUfabsT7zB5dKIRs05DqIHuR. To then change the connection you can do,

mutation {
  updateRemoteClusterConnection(input: {
    multiClusterViewName: "myMultiClusterView",
    connectionId: "CW8ppOz5CUfabsT7zB5dKIRs05DqIHuR",
    publicUrl: "https://remotelogscale2.example.com/"
  })
}

This changes the URL of the connection you created earlier. To verify that the change has been made you can list the connections as shown earlier or, since you know the ID of the connection, query that specific connection:

query {
  searchDomain(name: "myMultiClusterView") {
    remoteClusterConnection(id: "CW8ppOz5CUfabsT7zB5dKIRs05DqIHuR") {
      id
      ... on RemoteClusterConnection {
        publicUrl
      }
    }
  }
}

This will return something like

{
  "data": {
    "searchDomain": {
      "remoteClusterConnection": {
        "id": "CW8ppOz5CUfabsT7zB5dKIRs05DqIHuR",
        "publicUrl": "https://remotelogscale2.com/"
      }
    }
  }
}

You can also change the token this way by setting token.