In my case, no, it does not. In fact, for me, it makes the game so much better. For some, anyway. It depends on your name and what you think of it.
Personally, I love my real name (Seth). I love the sound of it, the look of it, how it's spelled, everything about it. I've always used my real name for my file name (even the first time I ever played a Zelda game, and had no idea the game would use my file name as the main character's name)
And, maybe it's because they both have four letters, but I think "Seth" flows just as well as "Link" would, perhaps even a bit better. Still one syllable, and it still fits well, in my opinion.
It always irks me when someone has entered their real name for Zelda and it just doesn't flow very well or have a heroic feel to it... Charlie or something like that. I like that name, but not for Link. In general, single syllable names work better, I believe. Like Seth or Drake.
In fact, I've gotten the image of Link being referred to as "Seth" "Seth, Hero of X" "Seth, chosen hero" that whenever I see Link, my mind doesn't click and think "Link." It immediately identifies that person as "Seth".