Using someone else's bank account would not only create problems for that specific person, but it would also put you in the spotlight as a potential money launderer, and trouble would begin for both of you. 100% effective anonymity does not exist, and if such anonymity existed, it would be lost the moment you want to send fiat to any bank.
I used LocalBitcoins quite a few years ago (the website still exists, but new registrations are not possible) and never had any problems.
Why I cannot register a new account?
LocalBitcoins has decided to stop providing Bitcoin trading services. New account registration was suspended on 2023-02-09.
At LocalBitcoins you could find people in your city to buy and sell Bitcoins, while the deposit remained blocked until the purchase/sale was satisfactory for both parties.
It's a shame you can't create an account to use that service, it's what you were looking for. I don't know if there are similar services, but you can always search for information.