I love it, but Im slightly biased as its one of my DD's middle names.
IMO, you shouldnt pick a name for the NN - unless you plan to call her that all the time? (My DD is Indianna but always been an Indie and doesnt even respond to Indianna!)
In my experience, different members of the family will come up with different nicknames anyway - your mum may call her Aria, your PIL's - Anna and yours/DP's siblings Ari.
But anyway, there are loads of NN's to get out of Arianna, and its a gorgeous name