Final answer:
A Transfer Agent is responsible for maintaining detailed records of shareholders and managing changes in stock ownership, not to be confused with Stockbrokers, Registrars, or Market Makers who serve different roles in the financial markets.
Step-by-step explanation:
An institution responsible for maintaining detailed records of shareholders and handling changes of ownership of stock is known as a Transfer Agent. This entity is tasked with ensuring that all records of share ownership are accurate, which includes recording changes in ownership when stock is bought and sold. Transfer agents also assist in managing lost, destroyed, or stolen certificates. Although other entities like Stockbrokers, Registrars, and Market Makers play significant roles in the finance world, it is the Transfer Agent that specifically deals with the maintenance of shareholder records and the administrative tasks related to transferring stock ownership.