Answer:
During the time of Shakespeare, last names were of utmost importance. Every person was recognized by the last name that he/she carried.
We can get hints from many of Shakespeare plays that during that time the last name described how the person will be looked upon in the eyes of other people.
Today, last names are still considered but they do not hold as much value as they did in the past. In many of the societies, a person is well-known for the actions he implements and the manners which he carries rather than the last name he holds.