Is it permissible to purchase a car through an Islamic bank if the bank buys the car and registers it in its name, then transfers ownership to me in exchange for a transfer fee and a specified profit margin?

There is no objection to purchasing a car from the bank at a price higher than the price at which the bank bought it, provided that the bank genuinely owns it and it falls under its guarantee. As for the transfer fees, if they are for documenting the second and first contracts, the first is permissible, but the second is not, because it is an obligation of what is not obligatory and taking money unjustly, resembling the forbidden earnest money (deposit).