If he wanted to create a link between the player and the game then it should be a free-roam game. If the player wants to immerse themselves and become who they want to be in the game they should be able to choose what they would like to do. In LoZ games there is always a set amount of things you must do to finish the game. It would be like me and my friend. We have the same name as eachother but does it make us fulfill eachother as people? No, we have common interests but are no completely alike. Same names are hardly a link if any at all.
the original LoZ was a 'free roam' or sandbox game, where you explored every nook and cranny and could defeat the dungeons totally out of order or even go 'swordless'.
Anyway, I usually name him Dink, or Stink. Sometimes my own name, or sometimes Grimmy. But usually Dink.
Well, when I was a kid on my second or third playthrough of OoT, for a joke I named him a name similar to link except with a wa instead of li (I was a child so I was allowed to be childish!) Now that’s sort of stuck and I call him that for every Zelda game I play
I usually just name him Emma, my name. But I did manage to accidentally hit another letter when I went to save the name one time without realizing it, and then had to go through the whole game as Emmaf.