This topic comes up quite often. Take a look through these threads to get started:

When did tradition of having a first-name and a surname come from? Was there a time when people only had one name? by /u/LadyOfTheLabyrinth

How did last names of colors arise (Blue, Green, Brown, White, Black, Grey), and why have I never seem anyone with the last names Red, Orange, Yellow, etc.? by /u/random-dent and /u/tim_mcdaniel

To add to the above, I offered some information on the practice as it developed in the Middle Ages in Italy: https://www.reddit.com/r/AskHistorians/comments/8gv854/around_what_time_period_did_last_names_become/dyfwsfw