All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
As a general rule, the crucial factor in the actualization of contracts is agreement and the occurrence of Eejaab (offer) and Qabool (acceptance).
Legal and administrative procedures, on the other hand, are purely for documentation. The fact that there was an error in the document does not negate the validity of the contract unless the parties of the contract withdraw, provided that their withdrawal is a legitimate consideration for withdrawing, since it is permissible to withdraw from some contracts due to them not being binding. These are called open contracts, and they include partnerships, agencies and the like. It is not permissible, on the other hand, to withdraw from binding contracts, such as sales and leasing contracts and the like if they are conducted legitimately without cause for withdrawal.
The fact that there is a mistake in legally registering the contract does not affect its validity from an Islamic point of view.
Allaah Knows best.