I’ll tell you what’s not mine: fav.
Let me explain why.
Almost any time I read it, I read it as though it rhymes with have. I know of course it’s supposed to rhyme with gave, to replicate the sound of that first syllable of favourite, but I can’t help it. There are no words in English which feature av without a vowel after them which rhyme with gave. Therefore, I can’t help reading it to sound like have.
There’s obviously a logic behind using fave instead, in that in more clearly looks like it should rhyme with gave (though there are words with similar spellings but different pronunciations, like have). I suppose people don’t like it though, as there’s no E after the V in favourite. Personally, I think including the E in fave is a perfectly reasonable compromise: it’s only an abbreviation, after all.
But I get why people don’t like including it and go with fav instead. It’ll never be my fav though.