Why do we have names?

Many centuries ago, people only had FIRST names. They were referred to by their father (Peter of William), or by occupation (Peter the Baker). Over time, more men were associated by their occupation (women had no occupations so they were known under their fathers, ex. Mary Anne of William).

Slowly, the intermediary connection ended. William the Lawyer became William Lawyer. John of John the Tanner became John Tanner. Where a son carried the father's first name, each name was appended with Sr or Jr.

The concept of 2-names became standard. John Black (who had ancestors in the blacksmith business) was no longer tied to an occupation he might not practice, but to a surname: Peter Baker; Patrick Seller; Joshua Merchant, etc.

Many centuries ago, society began to embody 2-names. But these also evolved into a practice of 3-names, often based on naming patterns within the family and society. First-born male carried the paternal grandfather's name as the first name; Second-born male, the maternal grandfather's name; First-born female, the maternal grandmother's name; second-born female, the paternal grandmother's name. Today, this is more often first-born male is named after the father.

Many centuries ago, a middle name was also started. Boy infants often were given a middle name that was their mother's maiden name. So a mother with a maiden name of Coltrix had a son George (after his dad) Coltrix (after his mother's line) and the father's surname.

By the 1800s, women who had children born out of wedlock gave the child the child's father's surname. This was because of inheritance rights. It wasn't until the 1900s that "out of wedlock" ran the risk of having a "bastard child", a vulgar term for illegitimate child, that laws restricted to only the woman's surname and the child being disinherited by law.

Today, naming practices have no set traditions.

Names allow us to be identified as individuals by others, both in a direct way and in reference to others. Where names are not unique, it is difficult but not impossible to discern the traits or accomplishments of different individuals. Even with two or more names (given, surname, middle name) there will be many people who have the same or confusingly similar names.
"Hey you with the brown hair! Not you, you! No the one in the baseball cap! No the other one!" See how confusing that would be?