While I prefer original characters like I said in a previous post, in fighting games and racing games like Smash and Kart, I actually vastly prefer playing as a Mii. Likewise, in simulation games like Harvest Moon and Animal Crossing, I feel that customization is needed. Harvest Moon is a little weird though, as I found out that the non-customizable characters, like the MC in
A Wonderful Life actually have names, they're just never mentioned in game. This has unfortunately put me in a weird position, as
A Wonderful Life, is one of my favorite Gamecube games, and when I think back on it, I see the mc as a Farmer version of me, so a dude named "Cody", yet apparently his name is "Mark" so now all I see when I look at him is a dude named "Mark." It's weird.
Pokemon, is kinda the same way, it's why I never bought the Hoenn remakes, even though that was my favorite generation of Pokemon or played any Pokemon games recently, as the minute a character has a name it's hard for me to rename them. Characters like Ryu from Breath of Fire, and Link though are different, even when I first introduced to both series I still felt it was wrong to rename them, especially Link.
I always name him my own name, since he's nothing but a cipher. The characters are all referring to you, talking to you; he's just the link between yourself and the game.
I feel like this may have been the case when the games were still 2D, but ever since then he's always felt more and more like his own person, even in the newer 2D games. This is apparently clear in the few games like FS/FSA and HW where you can't rename him, and the characters are directly referring to him by his name.