It's because it wasn't yet a memory of Alex for her at that point. There's a scene where she's in the bar with her girlfriend talking about something...I think it was her ex boyfriend...but after she finished talking she turns her head and has a moment where the memory of the kiss entered her mind where she now realizes it was Alex she actually kissed when a moment ago he was just a stranger all this time.
Watch that specific scene and you'll see her turn her head and whisper to herself "Oh!", in new recognition of that night. Up to that moment, she just always thought Alex was a random guy as she said to the ex boyfriend at the skating rink...but now through the letter writing, she figures out sitting at the bar that it was him. Then in the next scene she writes him asking why he didn't reveal himself to her that night.
It's like how the tree outside her apt complex instantly appeared in front of her when Alex planted it in 2004...so does her memories of Alex only enter her mind as their letter correspondence progresses. It's difficult to wrap your head around isn't it?
This is why she doesn't know who he is on Valentine's Day 2006...she hasn't yet begun writing the letters with him. I love movies like this that make you think like that. :)
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