I used to have some extended family who all went by nicknames unrelated to their legal names. It was a cultural thing.
For example, let's say a student named Fred Smith emails me, but then signs his name as "Alex Harrison." And his self-selected email address is alexrogers@school.edu. I'm not sure if it's a trend or a culture thing to use multiple names and last names, but it gets a bit confusing at times.
Both my sons have a couple of nicknames each, which come out depending on the situation. They're 3 & 6 now and are both called wee man by way of greeting. The youngest is now getting called Mac because his nickname is MacMonkey McBean. Names evolve over time.
You really need to be careful with lying to yourself like that. Being a whole integrated person who doesn't have to remember who he is and what lies he's told comes in handy.
If you measure by being a decent and content person, I'd have to say no.
Actually, that's not exactly what the story contained. It said that John was the legal name, but it didn't say that Jake wasn't the legal name. That happens all the time, John Jake Johnson, for example.