If you are talking about the United States during the time of the Great Depression, then the best answer to this question is President Franklin D. Roosevelt. He is the person who is generally given the most credit for restoring Americans’ faith in their banking system.
One major problem during the first few years of the Great Depression was the failure of many American banks. The banks had loaned out money to various people who lost their ability to repay the loans. As all these borrowers defaulted, the banks lost money. Depositors started to worry that their banks would lose their money so they often went to the banks to try to withdraw all of their savings. When too many depositors did this, the banks ran out of money and failed. This meant that most of their depositors lost all their savings. This created more runs on other banks, and the problem spiraled.
When President Roosevelt took office, one of his first acts was to try to stabilize the banking system. Almost immediately, he declared a “bank holiday,” suspending all bank transactions so people could not remove their money from the banks. By doing this, and by eventually doing other things like creating the FDIC to insure people’s deposits, FDR did much to restore Americans’ faith in their banking system. For this reason, he is the most likely answer to your question.