Yes. It is not uncommon for a moving company to use a subcontractor to perform all or a portion of the moving services. The primary moving company who booked the job may legally subcontract out the job to another properly licensed moving company to perform part or all of the services. Even if they use a subcontractor, the primary moving company will ultimately be responsible for the actions or omissions of the subcontractors. You should ask a moving company if they will use subcontractors before you sign a contract for services.