In most cases, no.
But…. There may be additional charges unknown at the start which are for example:
1) Difficult access on arrival and need a furniture lift, or a parking reservation
2) A visit of the customs (the handling of your belongings will be invoiced to you by the company on the spot)
3) Customs clearance impossible following an administrative problem (see next, to whom the fault is attributed, the customer or the mover)
4) Split delivery
5) Taxes applicable and payable directly to the customs of some countries of destination even in case of relocation and not determined at the outset.