No, but it's good practice to do so as with the fair side abbuting the boundary line, you have enclosed your land to the fullest extent and not gifted your neighbour the land between the fence posts.
If you pay for the fence you can choose which side you have facing your garden, it may be considered polite to give the neighbours the best view but it is rarely done these days.
Convention is to place the "nice looking side" toward the neighbour, but who is to say what the nice looking side is if you are doing panels with posts between.
I am going to be building a close board run of fencing and will place all the posts and rails my side, but this means I will be able to secure trelis and fix plants to my side.
As TheVictorian has said, if you are paying for it, then surely you should decide what to do? (within reason)
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