It's all about culture! Use the Balinese as your Model.
Some cultures already do this. Here's a link to Balinese naming conventions. Every first-born kid is named Wayan. And each kid after that gets a name specific to the order in which they were born. It's a bit like naming your kids First, Second and Third. These are more like titles, which tell people what your order is--within a family. Take a look at the link above, and you'll find that most of the names are actually titles. The names let anyone hearing them know your caste and rank. They are foreign unless you speak the language, but each name carries meaning as to your place in society--names that mean leader, and so on.
As to reasons for a naming system focused solely on profession, rank or caste, it would be prevalent in a society that values that more than individuality. That's your identity.
It can also be a vestige of an old society, and considered bad manners to use anything but a title (as Tezra pointed out).
Even in these societies, nicknames are prevalent, but they are reserved for those close to you, such as family or close friends, whose social rank is probably equivalent to yours or higher than yours. So, you might refer to an Aunt by her title out of respect, (although she might be the foreign minster or something, you would call her by her relationship to you, Aunt, because she outranks you within your family, although she might call you by a family nickname because you are of lower status to her, and her brother might use the family nickname for her) Anyone else, at a job, in public or anything else, would be called by their job/caste title.
There will be problems with this system, as there is in countries where people share names. The Balinese don't actually have surnames, BTW.
You might also want to take a look at naming conventions from Thailand. They don't follow the specific pattern, but it might be useful. Nicknames in in Thai cultures tend to be things like "Fat" (even if you were only chubby in childhood) or "Laughing One" or "Red" because your face was red as baby when you cried...
EDIT: Despite there being names in the Indian culture, I am going to recommend you read the book Kim By Rudyard Kipling. The way titles are used in this book and the way people refer to each other by status or title when they don't know each other (and even when they do) might be interesting to you. Plus, it's an awesome book. Bit racist (it's Kipling, and of a certain time, so is to be expected) but there's cultural stuff that tracks to what you're looking for: "Where are you from and what caste?" Is more important than "What is your name?" Most often, despite having names, people are called "Sahib" or "the lama" or "the Curator." And because Kim is a child of the streets, sometimes he will get a nickname right away, like "young tiger" from the ladies of the bazar or from the lama, "Chela" which means student/disciple. Just a good book to understand the cultural basis for titled people rather than named people, even if they do have proper names (like Kim) as well.