What is the ruling on buying an apartment from a bank by installments, where the bank first buys the apartment and then sells it by installments at a higher price, and it remains registered in the bank's name until the full amount is paid?

This transaction is permissible; it is a form of Murabaha sale. There is no harm in the apartment remaining registered in the bank's name, as this falls under the category of mortgaging the sold item with the seller to secure his right, and the apartment is, in reality, owned by the buyer.