Does this make me a official Zelda fan?

Yes I would say you are a official Zelda fan but the more Zelda games you complete the better fan you are so you are probably a Lvl 1 fan!

As the other guy said, you're probably a level 1 Zelda fan. You'd still count as a fan, but you don't rank as highly as other people. If you play more, you'll be considered more of a fan.

A lot of people own and have beaten OOT, so I can see why your friend would say that you aren't a real fan. Ocarina of Time is also considered one of the most "overrated" Zelda games as almost everyone cites it as their favourite. A lot of my friends have beaten Ocarina of Time, but that's like the only Zelda game they've played and it's the only one they know anything about. So they aren't true fans.

I don't like using myself as an example, but...

I have beaten all of the games except Zelda 2 (because it's hard as nails), Oracle of Ages, Four Swords Adventures and the Minish Cap. I own Zelda 2 but I don't own the other three (which is why I haven't beaten them).

I have lot's of Zelda merchandise (ie. posters, toys, books, shirts, bracelets, lunch boxes, console skins, calenders). I either preorder Zelda games or get them on the release day. I have Zelda songs on my ipod. My Skyrim character's name is Zelda. My Yahoo Answer's icon is Princess Zelda. I have Zelda on the brain! lol

So I'm a huge Zelda fan!

Well, do you enjoy any of the games in the series?

Yes?

Then you are a true Zelda fan.

Playing one game in the series, like the Zelda series in your case, doesn't constitute fanaticism...

When you've played around 4-5 out of the 14/15 games in the Zelda series, then you're more likely to be accepted by the fan club.

The only viable exception to this rule is when there's only a few number of titles in the series (like the Metroid Prime Trilogy, for example) OR when there's GAL (get-a-life) Timer involved, like in Pokémon... where a GAL timer in the 150+ hour range could be consider a fan of the game / series, but metrics for fanaticism will vary by game / series.

To beat Zelda is normal, but if you had fun to play, and want to play this anytime again, then you're a real fan, it does mean, you love Zelda.

If you like the game you're a fan.