In 1720 the British Parliament passed the Bubble Act which had specific regulations for securities.
However it was the failure of the Blue sky law and the 1930 financial crisis and Great Depression that led the United States government to pass legislation in 1934 to strengthen securities law and for the first time create a separate agency the Securities and Exchange Commission.
Typically, securities, banking and insurance are split, but there may also be separate agencies for futures, options and commodities.
They are often fully or partially funded by the organisations that are regulated through charges such as registration and licensing fees.
There is no common name for securities commission or financial regulatory agency in each country.
Most securities commissions have a mandate to protect consumers, make sure there is an orderly and stable financial market and that brokers and participants behave fairly with clients and each other.