When do you become a photographer? Let me answer a question with a question: "When does a boy become a man?"
It all depends on how you define "manhood."
Is it a definitive definition? Are you a man when you are 18 years old?
Is it a functional definition? Are you a man when you get married and have a family?
Is it a subjective definition? Are you a man when somebody calls you a man?
Is it defined by manifest reality? Are you a man when you can stand on your own two feet and say, "I am a man."
Are you a man when you learn how to hold you liquor? Are you a man when you join the military or fire a gun? Are you a man when you can drive a car?
The answer is "Yes" to all of the above.
The answer to the question of when you become a photographer is similar.
You can be a photographer when you learn how to use a camera and produce good photographs. You can be a photographer when you go into business and generate income. You can be a photographer when somebody else calls you one or you can be a photographer when you can stand up and say, "I am a photographer."
The bottom line to both questions has less to do with some definition of manhood or when you are a photographer and more to do with how you are identified. You can both identify yourself and others can identify you. You can be a man when somebody else calls you a man just as well as you can stand on your own two feet and declare your own manhood. Similarly, you can be a photographer when somebody else calls you a photographer just as well as you can identify yourself as a photographer.
Personally, I have three criteria for defining a photographer:
1) You can use a camera and produce photographs. With bias toward traditional photography or, at least, having a working understanding of traditional photography.
2) You identify yourself as a photographer, either verbally or with business cards and advertising.
3) Others recognize you as a photographer without you prompting them.
The first two are simple. Pick up a camera and hang out your shingle. Anybody can do that but, even if you can use your equipment to produce good photos and even if you take out a full page ad in the newspaper, I don't think you've made it. Close but not quite.
I think #3 is the key. Somebody you know or who you have made acquaintance must say, "My friend is a photographer." They don't necessarily have to say, "He's a photographer." Even then, I don't think you've fully satisfied the terms of point #3.
In addition to verbalizing it, I think, to fully satisfy the definition of "photographer," somebody has to see your pictures and like one of them well enough to voluntarily display it in their house, office or personal space.
As I said above, you are truly a photographer when you make a photograph that somebody else wants to hang on their wall without you asking them.