It doesn't really matter in any way but how you want it to look like. Other than that if you're going to send a msg to someone you don't have on your friends list you can simply type their name in lowercase and it will accept it.
Just as ugg ultimate said no one else can use your name spelled like yours and it doesn't matter whether lowercase or uppercase.
The One cannot be used by someone else, whether written the one or ThE oNe lol. Dont matter.
Just clarifying that's all.