The wizarding bank shown in the Harry Potter films is Gringotts.
Gringotts Wizarding Bank is located in Diagon Alley and is operated by goblins. Harry first visits it in Harry Potter and the Philosopher’s Stone with Rubeus Hagrid, who takes him to withdraw money and collect a mysterious package from a high-security vault.
The bank returns throughout the series as a place for wizarding currency, vaults and important secrets. In Harry Potter and the Deathly Hallows – Part 2, Harry, Ron and Hermione break into the Lestrange vault to destroy Helga Hufflepuff’s cup, one of Voldemort’s Horcruxes.
Gringotts is not a shop. Ollivanders sells wands, Flourish and Blotts sells books, and Madam Malkin’s provides robes. The name is commonly shortened to Gringotts, although the full name is Gringotts Wizarding Bank.