What is the ruling on taking a loan from a bank in my name—with shares being sold and their price given to my brother—on the condition that my brother repays the full installments to the bank, knowing that he will pay back more than what was taken?

The original transaction is Tawarruq in shares, and calling it a loan is incorrect. If the conditions for the permissibility of the transaction are met, then there is no harm in entering into it as an act of kindness towards the brother, and giving him the money would be in the form of a loan. So, if he buys the shares for 100,000 and sells them for 90,000, he then lends his brother 90,000, and the brother bears the remaining 10,000; because the lender is a benefactor and does not incur a loss, and there is no loan here that draws a benefit except for the benefit in the afterlife.