I find it very nny. I really dislike short (letter wise) fns as well.
Kai is really the only name short of 5 letters I like as a full name (and even then, I never see myself using it).
Liv reminds me of live - and kind of comes across as a very energic, lively personality. It would seem weird as a full name on someone who was calm and not so energic.
As a nn, its cute - as a full name, I really cant see it on anyone, any age, unless they are very lively.
But thats just me