Yes, you'll receive the contact information several times, as detailed below.
When you submit a booking request you will be given the contact information for the movers, both on the confirmation screen and in the booking request confirmation email.
A booking request becomes a reservation once the request is accepted.
Approximately 72 hours before your scheduled move date you will receive a reservation reminder email. This email will contain a summary of your move details as well as the contact details for your mover. You should contact them directly if you need to request changes, ask questions, or to receive status updates about their arrival time.