Relocation companies or Packers and Movers responsibly did job of Packing and Moving. They will pack the entire items of a house and move it to the another destination. So, those people are simple called relocation agents.
Next is Transporter: As name implies one who transport items (be it house hold or any other goods) from one place to another is called transporter.
Last one mentioned is House Shifting agents: As you know that house shifting companies an packers and mover companies are functionally same and the only one difference is most of them do not do packing instead they do shifting job only.